{"id":6716,"date":"2021-07-21T00:04:01","date_gmt":"2021-07-20T15:04:01","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6716"},"modified":"2021-12-22T09:43:17","modified_gmt":"2021-12-22T00:43:17","slug":"describing-graphs","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/describing-graphs\/","title":{"rendered":"\ud568\uc218\uc758 \uadf8\ub798\ud504"},"content":{"rendered":"<div style=\"display: none; visibility: hidden;\">\n<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<p><!--\n\\[\n\\newcommand{\\vecf}{{\\mathbf{f}}}\n\\newcommand{\\vecL}{{\\mathbf{L}}}\n\\newcommand{\\vecR}{{\\mathbb{R}}}\n\\newcommand{\\imI}{\\boldsymbol{i}}\n\\]\n-->\n<\/div>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 5\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p>\uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \ud568\uc218\uc758 \uadf9\uac12, \ud3c9\uade0\uac12 \uc815\ub9ac, \ud568\uc218\uc758 \uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131\uc744 \uc0b4\ud3b4\ubd05\ub2c8\ub2e4. \uc774 \ud3ec\uc2a4\ud2b8\ub294 \ubbf8\uc801\ubd84\ud559\uc744 \ucc98\uc74c \uacf5\ubd80\ud558\ub294 \uc0ac\ub78c\uc744 \ub300\uc0c1\uc73c\ub85c \ud558\ub294 \ub0b4\uc6a9\uc744 \ub2e4\ub8e8\uba70, \uc815\ub9ac\uc758 \uc99d\uba85\uc744 \uc9c1\uad00\uc801\uc778 \ubc29\ubc95\uc73c\ub85c \uc124\uba85\ud569\ub2c8\ub2e4. \uc5c4\ubc00\ud55c \uc815\uc758\uc640 \uc99d\uba85\uc744 \ubcf4\uace0\uc790 \ud55c\ub2e4\uba74 \ub2e4\uc74c \uae00\uc744 \ubcf4\uae30 \ubc14\ub78d\ub2c8\ub2e4.<\/p>\n<ul>\n<li><a href=\"https:\/\/sasamath.com\/blog\/articles\/calculus-the-mean-value-theorem\">\ud3c9\uade0\uac12 \uc815\ub9ac (SASA Math)<\/a><\/li>\n<li><a href=\"https:\/\/sasamath.com\/blog\/articles\/calculus-concavity-and-curve-sketching\">\ud568\uc218\uc758 \ubcfc\ub85d\uc131\uacfc \uadf8\ub798\ud504\uc758 \ubaa8\uc591 (SASA Math)<\/a><\/li>\n<\/ul>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ud568\uc218\uc758 \uadf9\uac12<\/h2>\n<p>\\(I = [a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uba70 \ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc2e4\ud568\uc218\uc774\uace0 \\(c\\in I\\)\ub77c\uace0 \ud558\uc790. \uc774\ub54c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n<ul>\n<li>\ub9cc\uc57d \uc784\uc758\uc758 \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x) \\le f(c)\\)\uc774\uba74, \u201c\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c <span class=\"defined\">\ucd5c\ub313\uac12\uc744 \uac00\uc9c4\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud558\uace0, \\(f(c)\\)\ub97c <span class=\"defined\">\ucd5c\ub313\uac12<\/span>(maximum value)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<li>\ub9cc\uc57d \uc784\uc758\uc758 \\(x\\in I\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x) \\ge f(c)\\)\uc774\uba74, \u201c\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c <span class=\"defined\">\ucd5c\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud558\uace0, \\(f(c)\\)\ub97c <span class=\"defined\">\ucd5c\uc19f\uac12<\/span>(minimum value)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(c\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \uc5f4\ub9b0\uad6c\uac04 \\(J\\)\uac00 \uc874\uc7ac\ud558\uc5ec, \\(I\\cap J\\)\uc5d0\uc11c \\(f\\)\uc758 \ucd5c\ub313\uac12\uc774 \\(f(c)\\)\uac00 \ub418\uba74, \u201c\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c <span class=\"defined\">\uadf9\ub313\uac12\uc744 \uac00\uc9c4\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. (local maximum)<\/li>\n<li>\ub9cc\uc57d \\(c\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \uc5f4\ub9b0\uad6c\uac04 \\(J\\)\uac00 \uc874\uc7ac\ud558\uc5ec, \\(I\\cap J\\)\uc5d0\uc11c \\(f\\)\uc758 \ucd5c\uc19f\uac12\uc774 \\(f(c)\\)\uac00 \ub418\uba74, \u201c\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c <span class=\"defined\">\uadf9\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4<\/span>\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. (local minimum)<\/li>\n<li>\uadf9\ub313\uac12\uacfc \uadf9\uc19f\uac12\uc744 \ud1b5\ud2c0\uc5b4 <span class=\"defined\">\uadf9\uac12<\/span>(local extremum)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/li>\n<\/ul>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.1.<\/span><br \/>\n\ud568\uc218 \\(y=f(x)\\)\uc758 \uadf8\ub798\ud504\uac00 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\ub2e4\uace0 \ud558\uc790.<\/p>\n<div class=\"margintop1 marginbottom1\"><a href=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1.png\" data-rel=\"penci-gallery-image-content\" ><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1.png\" alt=\"\" width=\"371\" height=\"176\" class=\"aligncenter size-full wp-image-7791\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1.png 1114w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1-300x142.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1-1024x486.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1-768x365.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_1-585x278.png 585w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/a><\/div>\n<p>\ud568\uc218 \\(f\\)\uac00 \uadf9\ub313\uac12\uc744 \uac16\ub294 \uc810\uc740 \\(x_2 ,\\) \\(x_4 ,\\) \\(x_7\\)\uc774\uba70, \\(f\\)\uac00 \uadf9\uc19f\uac12\uc744 \uac16\ub294 \uc810\uc740 \\(x_1 ,\\) \\(x_3 ,\\) \\(x_5 ,\\) \\(x_6\\)\uc774\ub2e4. \\(f\\)\ub294 \\(x_7\\)\uc5d0\uc11c \ucd5c\ub313\uac12 \\(M\\)\uc744 \uac00\uc9c0\uba70, \\(x_1\\)\uc5d0\uc11c \ucd5c\uc19f\uac12 \\(m\\)\uc744 \uac00\uc9c4\ub2e4. \\(x_8\\)\uc5d0\uc11c \\(f\\)\ub294 \uadf9\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n<p>\uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub41c \ud568\uc218 \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud55c \uacbd\uc6b0, \ubbf8\ubd84\uacc4\uc218\ub97c \uc774\uc6a9\ud558\uc5ec \\(f\\)\uac00 \uadf9\uac12\uc744 \uac00\uc9c8 \ub9cc\ud55c \uc810\uc744 \ucc3e\uc744 \uc218 \uc788\ub2e4.<\/p>\n<p>\\(f\\)\uac00 \uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uace0 \\(c\\in (a,\\,b)\\)\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\ub313\uac12\uc744 \uac00\uc9c0\uba70, \\(c\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(c\\)\uc5d0\uc11c \\(f\\)\uc758 \uc88c\ubbf8\ubd84\uacc4\uc218\ub294<br \/>\n\\[f_l &#8216; (c) = \\lim_{\\Delta x \\rightarrow 0^-} \\frac{f(c+\\Delta x) &#8211; f(c)}{\\Delta x} \\ge 0\\]<br \/>\n\uc774\uace0, \\(c\\)\uc5d0\uc11c \\(f\\)\uc758 \uc6b0\ubbf8\ubd84\uacc4\uc218\ub294<br \/>\n\\[f_r &#8216; (c) = \\lim_{\\Delta x \\rightarrow 0^+} \\frac{f(c+\\Delta x) &#8211; f(c)}{\\Delta x} \\le 0\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7f0\ub370 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ubbc0\ub85c<br \/>\n\\[f &#8216; (c) = f_l &#8216; (c) = f_r &#8216; (c)\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(f &#8216; (c) = 0\\)\uc774\ub2e4.<\/p>\n<p>\\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uc19f\uac12\uc744 \uac16\ub294 \uacbd\uc6b0\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \\(f &#8216; (c) =0\\)\uc774\ub77c\ub294 \uacb0\ub860\uc744 \uc5bb\ub294\ub2e4.<\/p>\n<p>\uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.1.<\/span><br \/>\n\ud568\uc218 \\(f\\)\uac00 \\(c\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \ud55c \uc5f4\ub9b0\uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \ub9cc\uc57d \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\uace0 \\(c\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uba74, \\(f &#8216; (c) = 0\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.2.<\/span><br \/>\n\\(f(x) =x^3 +x\\)\ub77c\uace0 \ud558\uc790. \\(f &#8216; (x) = 3x^2 +1\\)\uc774\ubbc0\ub85c \uc784\uc758\uc758 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(f &#8216; (x) > 0\\)\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(f\\)\ub294 \uc5b4\ub290 \uc810\uc5d0\uc11c\ub3c4 \uadf9\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n<p>\uc815\ub9ac 5.3.1\uc758 \uc5ed\uc740 \uc131\ub9bd\ud558\uc9c0 \uc54a\uc744 \uc218 \uc788\ub2e4. \ub2e4\uc74c \uc608\ub97c \ubcf4\uc790.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.3.<\/span><br \/>\n\\(g(x)=x^3\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(g &#8216; (x) = 3x^2\\)\uc774\ubbc0\ub85c, \\(g &#8216; (x)=0\\)\uc778 \uc810\uc740 \\(x=0\\) \ubfd0\uc774\ub2e4. \uadf8\ub7f0\ub370 \\(x_1 < x_2\\)\uc77c \ub54c \\( (x_1 )^3 < (x_2)^3 \\)\uc774\ubbc0\ub85c \\(g\\)\ub294 \ubaa8\ub4e0 \uacf3\uc5d0\uc11c \uc21c\uc99d\uac00\ud55c\ub2e4. \uc989 \\(g\\)\ub294 \\(0\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ud3c9\uade0\uac12 \uc815\ub9ac<\/h2>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uace0 \uc774 \uad6c\uac04\uc5d0\uc11c \uc5f0\uc18d\uc774\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\((a,\\,b)\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f(a) = f(b)\\)\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790.<\/p>\n<p>\ub9cc\uc57d \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc0c1\uc218\ud568\uc218\ub77c\uba74 \\((a,\\,b)\\)\uc758 \ubaa8\ub4e0 \uc810 \\(c\\)\uc5d0\uc11c \\(f &#8216; (c)=0\\)\uc774\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(f\\)\uac00 \\([a,\\,b]\\)\uc5d0\uc11c \uc0c1\uc218\ud568\uc218\uac00 \uc544\ub2c8\ub77c\uba74 \\(f\\)\uac00 \uadf9\uac12\uc744 \uac16\ub294 \uc810 \\(c\\)\uac00 \\((a,\\,b)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uadf8\ub7ec\uba74 \uc815\ub9ac 5.3.1\uc5d0 \uc758\ud558\uc5ec \\(f &#8216; (c)=0\\)\uc774\ub2e4.<\/p>\n<p>\uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.2. (\ub864\uc758 \uc815\ub9ac; Rolle&#8217;s Theorem)<\/span><\/p>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \ub2eb\ud78c\uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uace0 \uc774 \uad6c\uac04\uc5d0\uc11c \uc5f0\uc18d\uc774\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\((a,\\,b)\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f(a) = f(b)\\)\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f &#8216; (c)=0\\)\uc778 \uc810 \\(c\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\((a,\\,b)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\uc704 \uc815\ub9ac\ub97c \ub354 \uc77c\ubc18\uc801\uc778 \uacbd\uc6b0\ub85c \ud655\uc7a5\ud560 \uc218 \uc788\ub2e4. \uc815\ub9ac 5.3.2\uc5d0\uc11c\uc640 \uac19\uc740 \uc870\uac74\uc774 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \ub2e8 \\(f(a) = f(b)\\)\ub77c\ub294 \uc870\uac74\uc740 \ube7c\uc790. \uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \ud568\uc218 \\(g\\)\uc640 \\(h\\)\ub97c<br \/>\n\\[g(x) = \\frac{f(b)-f(a)}{b-a} (x-a) +f(a)\\]<br \/>\n\uadf8\ub9ac\uace0<br \/>\n\\[h(x) = f(x)-g(x)\\]<br \/>\n\ub77c\uace0 \uc815\uc758\ud558\uc790. \uadf8\ub7ec\uba74 \\(h\\)\ub294 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \\((a,\\,b)\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uba70 \\(h(a)=h(b)\\)\uac00 \uc131\ub9bd\ud55c\ub2e4. \ub530\ub77c\uc11c \ub864\uc758 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec \\(h &#8216; (c)=0\\)\uc778 \uc810 \\(c\\)\uac00 \\((a,\\,b)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uadf8\ub7f0\ub370<br \/>\n\\[h &#8216; (c) = f &#8216; (c) &#8211; g &#8216; (c) = f &#8216; (c) &#8211; \\frac{f(b) -f(a)}{b-a}\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[\\frac{f(b)-f(a)}{b-a} = f &#8216; (c)\\]<br \/>\n\ub97c \uc5bb\ub294\ub2e4. \uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.3. (\ud3c9\uade0\uac12 \uc815\ub9ac; The Mean Value Theorem)<\/span><\/p>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \ub2eb\ud78c\uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \ub9cc\uc57d \\(f\\)\uac00 \ub2eb\ud78c\uad6c\uac04 \\([a,\\,b]\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\uace0 \uc5f4\ub9b0\uad6c\uac04 \\((a,\\,b)\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uba74,<br \/>\n\\[\\frac{f(b)-f(a)}{b-a} = f &#8216; (c)\\]<br \/>\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(c\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\((a,\\,b)\\)\uc5d0 \uc874\uc7ac\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\ud3c9\uade0\uac12 \uc815\ub9ac\ub294 \ubbf8\ubd84\uacc4\uc218\ub97c \uc774\uc6a9\ud558\uc5ec \ud568\uc218\uc758 \uc131\uc9c8\uc744 \ubc1d\ud788\ub294 \ub370\uc5d0 \uc790\uc8fc \uc0ac\uc6a9\ub41c\ub2e4. \uc774\uc5b4\uc9c0\ub294 \ub0b4\uc6a9\uc744 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ud568\uc218\uc758 \uc99d\uac00\uc640 \uac10\uc18c<\/h2>\n<p>\\(I\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc2e4\ud568\uc218\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790. \ub9cc\uc57d \\(x_1\\)\uacfc \\(x_2\\)\uac00 \\(I\\)\uc5d0 \uc18d\ud55c \uc810\uc774\uace0 \\(x_1 < x_2\\)\uc774\uba74, \ud3c9\uade0\uac12 \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec\n\\[\\frac{f(x_2 ) - f(x_1 )}{x_2 - x_1} = f ' (c)\\]\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc810 \\(c\\)\uac00 \\(x_1\\)\uacfc \\(x_2\\) \uc0ac\uc774\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uc989\n\\[f(x_2 ) - f(x_1 ) = f ' (c) (x_2 - x_1 )\\]\n\uc774\ub2e4. \uc774 \uc2dd\uc73c\ub85c\ubd80\ud130 \\(f(x_2 ) - f(x_1 )\\)\uc758 \ubd80\ud638\uc640 \\(f ' (c)\\)\uc758 \ubd80\ud638\uac00 \uc77c\uce58\ud568\uc744 \uc54c \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \ub2e4\uc74c \uacb0\ub860\uc744 \uc5bb\ub294\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.4. (\ud568\uc218\uc758 \uc99d\uac10\uc5d0 \ub300\ud55c \uc77c\uacc4\ub3c4\ud568\uc218 \ud310\uc815\ubc95)<\/span><\/p>\n<p>\\(I\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub41c \uc2e4\ud568\uc218\ub77c\uace0 \ud558\uc790. \ub610\ud55c \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790.<\/p>\n<ol class=\"bracket\">\n<li>\ub9cc\uc57d \\(I\\)\uc758 \ubaa8\ub4e0 \uc810 \\(x\\)\uc5d0\uc11c \\(f &#8216; (x) > 0\\)\uc774\uba74, \\(f\\)\ub294 \\(I\\)\uc5d0\uc11c \uc21c\uc99d\uac00\ud55c\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(I\\)\uc758 \ubaa8\ub4e0 \uc810 \\(x\\)\uc5d0\uc11c \\(f &#8216; (x) < 0\\)\uc774\uba74, \\(f\\)\ub294 \\(I\\)\uc5d0\uc11c \uc21c\uac10\uc18c\ud55c\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(I\\)\uc758 \ubaa8\ub4e0 \uc810 \\(x\\)\uc5d0\uc11c \\(f &#8216; (x) = 0\\)\uc774\uba74, \\(f\\)\ub294 \\(I\\)\uc5d0\uc11c \uc0c1\uc218\ud568\uc218\uc774\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<p>\ub9cc\uc57d \ud568\uc218 \\(f\\)\uac00 \uc810 \\(c\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \ud55c \uc5f4\ub9b0\uad6c\uac04\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f &#8216; (c)=0\\)\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(c\\) \uadfc\ucc98\uc5d0\uc11c \ud568\uc218\uc758 \uadf8\ub798\ud504\uc758 \ubaa8\uc591\uc740 \ub2e4\uc74c \ub124 \uac00\uc9c0 \uacbd\uc6b0\uac00 \uc788\ub2e4.<\/p>\n<div class=\"margintop1 marginbottom1\">\n<a href=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345.png\" alt=\"\" width=\"661\" height=\"144\" class=\"aligncenter size-full wp-image-7800\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345.png 1982w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-300x66.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-1024x224.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-768x168.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-1536x336.png 1536w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-1920x419.png 1920w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-1170x256.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_2345-585x128.png 585w\" sizes=\"(max-width: 661px) 100vw, 661px\" \/><\/a>\n<\/div>\n<p>\ub530\ub77c\uc11c \\(c\\) \uadfc\ucc98\uc5d0\uc11c \\(f &#8216; \\)\uc758 \ubd80\ud638\uc758 \ubcc0\ud654\ub97c \uc0b4\ud54c\uc73c\ub85c\uc368 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\ub294\uc9c0 \uc5ec\ubd80\ub97c \uc870\uc0ac\ud560 \uc218 \uc788\ub2e4. \ub354\uc6b1\uc774 \\(c\\)\uc5d0\uc11c \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud558\uc9c0 \uc54a\uace0 \\(c\\) \uadfc\ucc98\uc5d0\uc11c \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud558\uae30\ub9cc \ud558\uc5ec\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \\(f &#8216; \\)\uc758 \ubd80\ud638\uc758 \ubcc0\ud654\ub97c \uc0b4\ud54c\uc73c\ub85c\uc368 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\ub294\uc9c0 \uc5ec\ubd80\ub97c \uc870\uc0ac\ud560 \uc218 \uc788\ub2e4. \uc774 \uc0ac\uc2e4\uc744 \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.5. (\ud568\uc218\uc758 \uadf9\uac12\uc5d0 \ub300\ud55c \uc77c\uacc4\ub3c4\ud568\uc218 \ud310\uc815\ubc95)<\/span><\/p>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uc810 \\(c\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \ud55c \uc5f4\ub9b0\uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \\(c\\)\ub97c \uc81c\uc678\ud55c \ubaa8\ub4e0 \uc810\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790. (\\(c\\)\uc5d0\uc11c \\(f\\)\ub294 \ubbf8\ubd84 \uac00\ub2a5\ud560 \uc218\ub3c4 \uc788\uace0 \uc544\ub2d0 \uc218\ub3c4 \uc788\ub2e4.)<\/p>\n<ol class=\"bracket\">\n<li>\\(x\\)\uc758 \uac12\uc774 \\(c\\)\uc758 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc9c0\ub0a0 \ub54c \\(f &#8216; (x)\\)\uc758 \ubd80\ud638\uac00 \uc74c\uc5d0\uc11c \uc591\uc73c\ub85c \ubc14\ub00c\uba74 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4.<\/li>\n<li>\\(x\\)\uc758 \uac12\uc774 \\(c\\)\uc758 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc9c0\ub0a0 \ub54c \\(f &#8216; (x)\\)\uc758 \ubd80\ud638\uac00 \uc591\uc5d0\uc11c \uc74c\uc73c\ub85c \ubc14\ub00c\uba74 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\ub313\uac12\uc744 \uac00\uc9c4\ub2e4.<\/li>\n<li>\\(x\\)\uc758 \uac12\uc774 \\(c\\)\uc758 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uc9c0\ub0a0 \ub54c \\(f &#8216; (x)\\)\uc758 \ubd80\ud638\uac00 \ubc14\ub00c\uc9c0 \uc54a\uc73c\uba74 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uace0 \\(c\\)\uac00 \\(I\\)\uc758 \uc810\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(f &#8216; (c)=0\\)\uc774\uac70\ub098 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \ubbf8\ubd84 \ubd88\uac00\ub2a5\ud558\uba74, \\(c\\)\ub97c \\(f\\)\uc758 <span class=\"defined\">\uc784\uacc4\uc810<\/span>(critical point)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. (\uc784\uacc4\uc810\uc740 \uadf8\ub798\ud504 \uc704\uc758 \uc810\uc774 \uc544\ub2c8\ub77c \uc815\uc758\uc5ed\uc758 \uc810\uc774\ub77c\ub294 \uc0ac\uc2e4\uc744 \uc8fc\uc758\ud558\uc790.)<\/p>\n<p>\uc815\ub9ac 5.3.5\uc5d0 \uc758\ud558\uba74 \ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uc744 \ub54c \\(f\\)\uac00 \uadf9\uac12\uc744 \uac16\ub294 \uc810\uc740 \uc784\uacc4\uc810\uacfc \\(I\\)\uc758 \uc591 \ub05d\uc810 \ubfd0\uc774\ub2e4. \uc774 \uc0ac\uc2e4\uc744 \uc774\uc6a9\ud558\uc5ec \ud568\uc218\uac00 \uadf9\uac12\uc744 \uac16\ub294 \uc810\uc744 \uc870\uc0ac\ud560 \uc218 \uc788\ub2e4. \ub2e4\uc74c \uc608\ub97c \ubcf4\uc790.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.4.<\/span><br \/>\n\ud568\uc218 \\(f\\)\uac00 \uad6c\uac04 \\([1,\\,5]\\)\uc5d0\uc11c<br \/>\n\\[f(x) = -x^2 +4x+3\\]<br \/>\n\uc73c\ub85c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(f\\)\ub294 \\([1,\\,5]\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0<br \/>\n\\[f &#8216; (x) = -2x+4\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(f &#8216; (x)=0\\)\uc778 \uc810\uc740 \\(x=2\\) \ubfd0\uc774\ub2e4. \uc774 \uc810\uc5d0\uc11c \ud568\uc22b\uac12\uc740 \\[f(2)=7\\]\uc774\ub2e4.<\/p>\n<p>\ub2e4\uc74c\uc73c\ub85c \uad6c\uac04\uc758 \ub05d\uc810\uc5d0\uc11c \ud568\uc22b\uac12\uc740 \\[f(1) = 6 ,\\quad f(5)=-2\\]\uc774\ub2e4.<\/p>\n<p>\uadf8\ub7ec\ubbc0\ub85c \\([1,\\,5]\\)\uc5d0\uc11c \\(f\\)\ub294 \ucd5c\ub313\uac12 \\(f(2)=7\\)\uc744 \uac00\uc9c0\uba70, \ucd5c\uc19f\uac12 \\(f(5)=-2\\)\ub97c \uac00\uc9c4\ub2e4.\n<\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131<\/h2>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\uace0, \uc774 \uad6c\uac04\uc5d0\uc11c \uc5f0\uc18d\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \uc774 \ud568\uc218\uc758 \uadf8\ub798\ud504 \uc704\uc758 \uc784\uc758\uc758 \ub450 \uc810\uc744 \uc774\uc5c8\uc744 \ub54c \uadf8 \uc120\ubd84\uc774 \uadf8\ub798\ud504\uc758 \uc544\ub798\ucabd\uc5d0 \ub193\uc774\uc9c0 \uc54a\uc73c\uba74 \u201c\\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 \uc544\ub798\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4. \ub9cc\uc57d \uc774 \ud568\uc218\uc758 \uadf8\ub798\ud504 \uc704\uc758 \uc784\uc758\uc758 \ub450 \uc810\uc744 \uc774\uc5c8\uc744 \ub54c \uadf8 \uc120\ubd84\uc774 \uadf8\ub798\ud504\uc758 \uc704\ucabd\uc5d0 \ub193\uc774\uc9c0 \uc54a\uc73c\uba74 \u201c\\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 \uc704\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4\u201d\ub77c\uace0 \ub9d0\ud55c\ub2e4.<\/p>\n<p>\ub9cc\uc57d \ud568\uc218 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uba74 \\(f\\)\uc758 \ub3c4\ud568\uc218\ub97c \uc774\uc6a9\ud558\uc5ec \\(f\\)\uc758 \uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \ud310\ubcc4\ud560 \uc218 \uc788\ub2e4.<\/p>\n<ul>\n<li>\ub3c4\ud568\uc218 \\(f &#8216; \\)\uac00 \\(I\\)\uc5d0\uc11c \uc99d\uac00\ud558\uba74 \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 <span class=\"defined\">\uc544\ub798\ucabd\uc73c\ub85c \ubcfc\ub85d<\/span>\ud558\ub2e4. (concave upward)<\/li>\n<li>\ub3c4\ud568\uc218 \\(f &#8216; \\)\uac00 \\(I\\)\uc5d0\uc11c \uac10\uc18c\ud558\uba74 \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 <span class=\"defined\">\uc704\ucabd\uc73c\ub85c \ubcfc\ub85d<\/span>\ud558\ub2e4. (concave downward)<\/li>\n<\/ul>\n<p>\uc774 \uc0c1\ud669\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uadf8\ub798\ud504\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\n<div class=\"margintop1 marginbottom1\">\n<a href=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67.png\" alt=\"\" width=\"410\" height=\"187\" class=\"aligncenter size-full wp-image-7799\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67.png 1231w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67-300x137.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67-1024x467.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67-768x350.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67-1170x533.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_67-585x267.png 585w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/a>\n<\/div>\n<p>\ub9cc\uc57d \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ub450 \ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uba74, \\(f\\)\uc758 \uc774\uacc4\ub3c4\ud568\uc218\uc758 \ud568\uc22b\uac12\uc758 \ubd80\ud638\ub97c \uc0ac\uc6a9\ud558\uc5ec \\(f\\)\uc758 \uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131\uc744 \ud310\uc815\ud560 \uc218 \uc788\ub2e4. \ub2e4\uc74c \uc815\ub9ac\ub97c \ubcf4\uc790.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.6. (\uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131\uc5d0 \ub300\ud55c \uc774\uacc4\ub3c4\ud568\uc218 \ud310\uc815\ubc95)<\/span><\/p>\n<p>\uc2e4\ud568\uc218 \\(f\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(I\\)\uc5d0\uc11c \\(f\\)\uac00 \ub450 \ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\uace0 \ud558\uc790.<\/p>\n<ol class=\"bracket\">\n<li>\ub9cc\uc57d \\(I\\)\uc758 \ubaa8\ub4e0 \uc810 \\(x\\)\uc5d0\uc11c \\(f &#8216; &#8216; (x) > 0\\)\uc774\uba74, \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 \uc544\ub798\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(I\\)\uc758 \ubaa8\ub4e0 \uc810 \\(x\\)\uc5d0\uc11c \\(f &#8216; &#8216; (x) < 0\\)\uc774\uba74, \\(I\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 \uc704\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.5.<\/span><br \/>\n\ud568\uc218 \\(f\\)\uac00 \uc774\ucc28\ud568\uc218\ub77c\uace0 \ud558\uc790. \uc989<br \/>\n\\[f(x) = ax^2 + bx + c , \\quad a \\ne 0\\]<br \/>\n\uc774\ub77c\uace0 \ud558\uc790. \\(f &#8216; &#8216; (x)= a\\)\uc774\ubbc0\ub85c \uadf8\ub798\ud504 \\(y=f(x)\\)\uc758 \ubcfc\ub85d\uc131\uc740 \\(a\\)\uc758 \ubd80\ud638\uc5d0 \uc758\ud558\uc5ec \uacb0\uc815\ub41c\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(a > 0\\)\uc774\uba74 \\(f\\)\uc758 \uadf8\ub798\ud504\ub294 \uc544\ub798\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\uba70, \\(a < 0\\)\uc774\uba74 \\(f\\)\uc758 \uadf8\ub798\ud504\ub294 \uc704\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4.\n<\/p>\n<\/div>\n<p>\ud568\uc218 \\(f\\)\uc758 \uadf8\ub798\ud504\uac00 \uc810 \\((c ,\\, f(c))\\)\uc5d0\uc11c \uc811\uc120\uc744 \uac00\uc9c0\uace0, \uadf8 \uc810\uc5d0\uc11c \uadf8\ub798\ud504\uac00 \ubcfc\ub85d\ud55c \ubc29\ud5a5\uc774 \ubc14\ub00c\uba74, \uc810 \\((c,\\,f(c))\\)\ub97c \\(f\\)\uc758 \uadf8\ub798\ud504\uc758 <span class=\"defined\">\ubcc0\uace1\uc810<\/span>(point of inflection)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.7. (\ubcc0\uace1\uc810\uc5d0\uc11c\uc758 \uc774\uacc4\ubbf8\ubd84\uacc4\uc218)<\/span><\/p>\n<p>\uc810 \\((c,\\,f(c))\\)\uac00 \ud568\uc218 \\(f\\)\uc758 \uadf8\ub798\ud504\uc758 \ubcc0\uace1\uc810\uc774\uba74, \\(f &#8216; &#8216; (c) = 0\\)\uc774\uac70\ub098 \ub610\ub294 \\(f &#8216; &#8216; (c)\\)\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.6.<\/span><br \/>\n\ub2e4\uc74c\uacfc \uac19\uc774 \uc8fc\uc5b4\uc9c4 \ud568\uc218 \\(g : \\mathbb{R} \\rightarrow \\mathbb{R}\\)\ub97c \uc0b4\ud3b4\ubcf4\uc790.<br \/>\n\\[g(x) = x^3 + x^2 + x\\]<br \/>\n\ud568\uc218 \\(g\\)\ub97c \ubbf8\ubd84\ud558\uba74<br \/>\n\\[g &#8216; (x) = 3x^2 +2x +1\\]<br \/>\n\uadf8\ub9ac\uace0<br \/>\n\\[g &#8216; &#8216; (x) = 6x + 2\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c \\(y=g(x)\\)\uc758 \uadf8\ub798\ud504\ub294 \\(x < - \\frac{1}{3}\\)\uc778 \ubc94\uc704\uc5d0\uc11c \uc544\ub798\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\uace0, \\(x > &#8211; \\frac{1}{3}\\)\uc778 \ubc94\uc704\uc5d0\uc11c \uc704\ucabd\uc73c\ub85c \ubcfc\ub85d\ud558\ub2e4. \uc810 \\(\\left( -\\frac{1}{3} ,\\, -\\frac{7}{27} \\right)\\)\uc740 \ud568\uc218 \\(g\\)\uc758 \uadf8\ub798\ud504\uc758 \ubcc0\uace1\uc810\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uc815\ub9ac 5.3.1\uc5d0\uc11c \ud568\uc218 \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \uc810 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac00\uc9c0\uba74 \\(f &#8216; (c)=0\\)\uc784\uc744 \uc0b4\ud3b4\ubcf4\uc558\ub2e4. \ub610\ud55c \uc815\ub9ac 5.3.5\uc5d0\uc11c \ub3c4\ud568\uc218 \\(f &#8216; \\)\uc758 \ubd80\ud638\uc758 \ubcc0\ud654\ub97c \uad00\ucc30\ud568\uc73c\ub85c\uc368 \\(f\\)\uac00 \\(c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\ub294\uc9c0 \uc5ec\ubd80\ub97c \ud310\ub2e8\ud560 \uc218 \uc788\uc5c8\ub2e4. \ub9cc\uc57d \\(f\\)\uac00 \ub450 \ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud558\uba74 \uc774\uacc4\ub3c4\ud568\uc218 \\(f &#8216; &#8216; \\)\uc758 \ubd80\ud638\ub97c \uad00\ucc30\ud568\uc73c\ub85c\uc368 \\(c\\)\uc5d0\uc11c \\(f\\)\uac00 \uadf9\uac12\uc744 \uac16\ub294\uc9c0 \uc5ec\ubd80\ub97c \ud310\ub2e8\ud560 \uc218 \uc788\ub2e4. \ub2e4\uc74c \uc815\ub9ac\ub97c \ubcf4\uc790.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 5.3.8. (\ud568\uc218\uc758 \uadf9\uac12\uc5d0 \ub300\ud55c \uc774\uacc4\ub3c4\ud568\uc218 \ud310\uc815\ubc95)<\/span><\/p>\n<p>\\(I\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uace0 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub41c \ud568\uc218\uc774\uba70, \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \uc774\uacc4\ub3c4\ud568\uc218\ub97c \uac00\uc9c4\ub2e4\uace0 \ud558\uc790. \\(c\\)\uac00 \\(I\\)\uc758 \uc548\ucabd\uc5d0 \uc787\ub294 \uc810\uc774\uace0 \\(f &#8216; (c) = 0\\)\uc774\ub77c\uace0 \ud558\uc790.<\/p>\n<ol class=\"bracket\">\n<li>\ub9cc\uc57d \\(f &#8216; &#8216; (c) < 0\\)\uc774\uba74, \\(f\\)\ub294 \\(x=c\\)\uc5d0\uc11c \uadf9\ub313\uac12\uc744 \uac00\uc9c4\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f &#8216; &#8216; (c) > 0\\)\uc774\uba74, \\(f\\)\ub294 \\(x=c\\)\uc5d0\uc11c \uadf9\uc19f\uac12\uc744 \uac00\uc9c4\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(f &#8216; &#8216; (c) = 0\\)\uc774\uba74, \uc774 \ud310\uc815\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \\(f\\)\uac00 \\(x=c\\)\uc5d0\uc11c \uadf9\uac12\uc744 \uac16\ub294\uc9c0 \uc5ec\ubd80\ub97c \ud310\uc815\ud560 \uc218 \uc5c6\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.7.<\/span><br \/>\n\ub2e4\uc74c\uacfc \uac19\uc774 \uc8fc\uc5b4\uc9c4 \ub2e4\ud56d\ud568\uc218 \\(h\\)\ub97c \uc0b4\ud3b4\ubcf4\uc790.<br \/>\n\\[h(x) = x^3 &#8211; 3x.\\]<br \/>\n\uc774 \ud568\uc218\ub97c \ubbf8\ubd84\ud558\uba74<br \/>\n\\[h &#8216; (x) = 3x^2 &#8211; 3\\]<br \/>\n\uadf8\ub9ac\uace0<br \/>\n\\[h &#8216; &#8216; (x) = 6x\\]<br \/>\n\uc774\ub2e4. \ubc29\uc815\uc2dd \\(h &#8216; (x) = 0\\)\uc744 \ud480\uba74 \\(x=-1\\) \ub610\ub294 \\(x=1\\)\uc774\ub2e4. \uadf8\ub7f0\ub370<br \/>\n\\[h &#8216; &#8216; (-1) = -6 < 0 ,\\quad h ' ' (1) = 6 > 0\\]<br \/>\n\uc774\ubbc0\ub85c, \\(h\\)\ub294 \\(-1\\)\uc5d0\uc11c \uadf9\ub313\uac12 \\(2\\)\ub97c \uac00\uc9c0\uba70, \\(1\\)\uc5d0\uc11c \uadf9\uc19f\uac12 \\(-2\\)\ub97c \uac00\uc9c4\ub2e4.\n<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 5.3.8.<\/span><br \/>\n\ub2e4\ud56d\ud568\uc218 \\(f\\)\uac00<br \/>\n\\[f(x)= x^4 + 4x^3\\]<br \/>\n\uc73c\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \ubbf8\ubd84\uc744 \uc774\uc6a9\ud558\uc5ec \uc774 \ud568\uc218\uc758 \uadf8\ub798\ud504\uc758 \uac1c\ud615\uc744 \uc870\uc0ac\ud574 \ubcf4\uc790.<\/p>\n<p>\uba3c\uc800 \\(f(x)\\)\uc758 \uc2dd\uc744 \uc778\uc218\ubd84\ud574\ud558\uba74<br \/>\n\\[f(x) = x^3 (x+4)\\]<br \/>\n\uc774\ub2e4. \ub2e4\uc74c\uc73c\ub85c \\(f\\)\ub97c \ubbf8\ubd84\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[\\begin{align}<br \/>\nf &#8216; (x) &#038;= 4x^3 + 12x^2 = 4x^2 (x+3) , \\\\[6pt]<br \/>\nf &#8216; &#8216; (x) &#038;= 12x^2 + 24x = 12x(x+2) .<br \/>\n\\end{align}\\]<br \/>\n\ub450 \ubc29\uc815\uc2dd <!-- \\(f(x)=0,\\) --> \\(f &#8216; (x) =0,\\) \\(f &#8216; &#8216; (x) =0\\)\uc758 \uadfc\uc744 \uad6c\ud558\uace0, \uc774 \uadfc\uc744 \uae30\uc900\uc73c\ub85c \ud45c\ub97c \ub9cc\ub4e4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"margintop1 margibottom1\">\n<a href=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/11\/ic_ex_5_3_8_table.png\" data-rel=\"penci-gallery-image-content\" ><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/11\/ic_ex_5_3_8_table.png\" alt=\"\" width=\"469\" height=\"116\" class=\"aligncenter size-full wp-image-7998\" \/><\/a>\n<\/div>\n<p>\uc774 \ud45c\ub97c \ubc14\ud0d5\uc73c\ub85c \ud568\uc218 \\(y=f(x)\\)\uc758 \uadf8\ub798\ud504\ub97c \uadf8\ub9ac\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<div class=\"margintop1 margibottom1\">\n<a href=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8.png\" data-rel=\"penci-gallery-image-content\" ><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8.png\" alt=\"\" width=\"238\" height=\"206\" class=\"aligncenter size-full wp-image-7798\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8.png 1429w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8-300x259.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8-1024x885.png 1024w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8-768x664.png 768w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8-1170x1011.png 1170w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/09\/ic_503_8-585x506.png 585w\" sizes=\"(max-width: 238px) 100vw, 238px\" \/><\/a>\n<\/div>\n<p>\ud45c\uc640 \uadf8\ub798\ud504\ub97c \ud1b5\ud574 \uc54c \uc218 \uc788\ub294 \\(f\\)\uc758 \uc131\uc9c8\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<ul>\n<li>\ud568\uc218 \\(f\\)\uc758 \uc784\uacc4\uc810\uc740 \\(-3\\)\uacfc \\(0\\)\uc774\ub2e4.<\/li>\n<li>\\(f\\)\ub294 \\(-3\\)\uc5d0\uc11c \ucd5c\uc19f\uac12 \\(-27\\)\uc744 \uac00\uc9c4\ub2e4.<\/li>\n<li>\\(-3\\) \uc774\uc678\uc758 \uc810\uc5d0\uc11c \\(f\\)\ub294 \uadf9\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c \\(f\\)\ub294 \ucd5c\ub313\uac12\uc744 \uac16\uc9c0 \uc54a\ub294\ub2e4.<\/li>\n<li>\\(f\\)\uc758 \uadf8\ub798\ud504\uc758 \ubcc0\uace1\uc810\uc740 \\((-2,\\,-16)\\)\uacfc \\((0,\\,0)\\)\uc774\ub2e4.<\/li>\n<\/ul>\n<\/div>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n\n\n\n<p>.<\/p>\n\n\n\n\n\n<p>.<\/p>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\u201c\u201d\n\u2018\u2019\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/differentiation-theorems\">\ubbf8\ubd84 \uacf5\uc2dd<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/elementary-transcendental-functions\">\uae30\ubcf8 \ucd08\uc6d4\ud568\uc218\uc758 \ubbf8\ubd84<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 5\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \ud568\uc218\uc758 \uadf9\uac12, \ud3c9\uade0\uac12 \uc815\ub9ac, \ud568\uc218\uc758 \uadf8\ub798\ud504\uc758 \ubcfc\ub85d\uc131\uc744 \uc0b4\ud3b4\ubd05\ub2c8\ub2e4. \uc774 \ud3ec\uc2a4\ud2b8\ub294 \ubbf8\uc801\ubd84\ud559\uc744 \ucc98\uc74c \uacf5\ubd80\ud558\ub294 \uc0ac\ub78c\uc744 \ub300\uc0c1\uc73c\ub85c \ud558\ub294 \ub0b4\uc6a9\uc744 \ub2e4\ub8e8\uba70, \uc815\ub9ac\uc758 \uc99d\uba85\uc744 \uc9c1\uad00\uc801\uc778 \ubc29\ubc95\uc73c\ub85c \uc124\uba85\ud569\ub2c8\ub2e4. \uc5c4\ubc00\ud55c \uc815\uc758\uc640 \uc99d\uba85\uc744 \ubcf4\uace0\uc790 \ud55c\ub2e4\uba74 \ub2e4\uc74c \uae00\uc744 \ubcf4\uae30 \ubc14\ub78d\ub2c8\ub2e4. \ud3c9\uade0\uac12 \uc815\ub9ac (SASA Math) \ud568\uc218\uc758 \ubcfc\ub85d\uc131\uacfc \uadf8\ub798\ud504\uc758 \ubaa8\uc591 (SASA Math) \ud568\uc218\uc758 \uadf9\uac12 \\(I = [a,\\,b]\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uad6c\uac04\uc774\uba70 \ud568\uc218&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":503,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6716","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6716","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6716"}],"version-history":[{"count":38,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6716\/revisions"}],"predecessor-version":[{"id":8337,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6716\/revisions\/8337"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}