{"id":5314,"date":"2025-01-08T19:59:20","date_gmt":"2025-01-08T10:59:20","guid":{"rendered":"https:\/\/torisetudy.com\/?p=5314"},"modified":"2026-03-09T17:49:53","modified_gmt":"2026-03-09T08:49:53","slug":"%e5%be%ae%e5%88%86%e6%b3%95","status":"publish","type":"post","link":"https:\/\/torisetudy.com\/?p=5314","title":{"rendered":"\u5fae\u5206\u6cd5"},"content":{"rendered":"\n<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u63a5\u7dda\u3068\u6cd5\u7dda<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u95a2\u6570\u306e\u5897\u6e1b<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u95a2\u6570\u306e\u6975\u5927\u3068\u6975\u5c0f<\/a><\/li><\/ul><\/div>\n<h2 class=\"wp-block-heading\"><span id=\"i\">\u63a5\u7dda\u3068\u6cd5\u7dda<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u63a5\u7dda<\/h3>\n\n\n\n<p>\u95a2\u6570 $f(x)$ \u306e\u5fae\u5206\u4fc2\u6570 $f\\mskip 2mu\\prime (a)$ \u306f\uff0c\u66f2\u7dda $y=f(x)$ \u4e0a\u306e\u70b9 $(a,\\,f(a))$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u50be\u304d\u3092\u8868\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u3088\u3063\u3066\uff0c\u66f2\u7dda $y=f(x)$ \u306e $x=a$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u66f2\u7dda $y=f(x)$ \u4e0a\u306e\u70b9 $(a,\\,f(a))$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$y=f^\\prime(a)(x-a)+f(a)$$<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u6cd5\u7dda<\/h3>\n\n\n\n<p>\u66f2\u7dda\u4e0a\u306e\u70b9 $(a,\\,f(a))$ \u3092\u901a\u308a\uff0c\u3053\u306e\u70b9\u306b\u304a\u3051\u308b\u305d\u306e\u66f2\u7dda\u306e\u63a5\u7dda\u3068\u5782\u76f4\u3067\u3042\u308b\u76f4\u7dda\u3092<span class=\"st-mymarker-s\">\u6cd5\u7dda<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u63a5\u7dda\u306e\u50be\u304d\u306f $f\\mskip 2mu\\prime (a)$ \u306a\u306e\u3067\uff0c\u6cd5\u7dda\u306e\u50be\u304d\u306f $f\\mskip 2mu\\prime (a)\\neq0$ \u306e\u3068\u304d\uff0c$-\\Bun{1}{f\\mskip 2mu\\prime (a)}$ \u3068\u8868\u305b\u307e\u3059\u3002\u3088\u3063\u3066\uff0c\u6cd5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c<\/p>\n\n\n\n<p>$$y=-\\bun{1}{f^\\prime(a)}(x-a)+f(a)$$\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i-2\">\u95a2\u6570\u306e\u5897\u6e1b<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u5897\u52a0\u95a2\u6570\u3068\u6e1b\u5c11\u95a2\u6570<\/h3>\n\n\n\n<p>\u95a2\u6570 $f(x)$ \u306b\u304a\u3044\u3066\uff0c\u3042\u308b\u533a\u9593\u3067 $x$ \u304c\u5897\u52a0\u3059\u308b\u3068 $f(x)$ \u3082\u5897\u52a0\u3059\u308b\u3068\u304d\uff0c$f(x)$ \u306f<span class=\"st-mymarker-s\">\u5358\u8abf\u5897\u52a0<\/span>\u3067\u3042\u308b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u9006\u306b\uff0c$x$ \u304c\u5897\u52a0\u3059\u308b\u3068 $f(x)$ \u306f\u6e1b\u5c11\u3059\u308b\u3068\u304d\uff0c$f(x)$ \u306f<span class=\"st-mymarker-s\">\u5358\u8abf\u6e1b\u5c11<\/span>\u3067\u3042\u308b\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u95a2\u6570\u306e\u5897\u6e1b\u306f\uff0c$f\\mskip 2mu\\prime (x)$ \u306e\u7b26\u53f7\u3067\u78ba\u8a8d\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>$f\\mskip 2mu\\prime (x)$ \u3068\u95a2\u6570\u306e\u5897\u6e1b<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u3042\u308b\u533a\u9593\u3067\uff0c\u5e38\u306b\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\begin{aligned}&amp;\\stext{$f\\mskip 2mu\\prime (x)&gt;0$ \u306a\u3089\u3070\uff0c$f(x)$ \u306f\u305d\u306e\u533a\u9593\u3067\u5358\u8abf\u5897\u52a0\u3059\u308b\u3002}\\\\&amp;\\stext{$f\\mskip 2mu\\prime (x)&lt;0$ \u306a\u3089\u3070\uff0c$f(x)$ \u306f\u305d\u306e\u533a\u9593\u3067\u5358\u8abf\u6e1b\u5c11\u3059\u308b\u3002}\\\\&amp;\\stext{$f\\mskip 2mu\\prime (x)=0$ \u306a\u3089\u3070\uff0c$f(x)$ \u306f\u305d\u306e\u533a\u9593\u3067\u5b9a\u6570\u3067\u3042\u308b\u3002}\\end{aligned}$$<\/p>\n<\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">\u5177\u4f53\u7684\u306a\u95a2\u6570\u3067<\/h3>\n\n\n\n<p>\u3053\u308c\u3092\u7528\u3044\u3066\uff0c$f(x)=x^3+3x^2-2$ \u306e\u5897\u6e1b\u3092\u8abf\u3079\uff0c$y=f(x)$ \u306e\u30b0\u30e9\u30d5\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u307e\u305a\uff0c$f\\mskip 2mu\\prime (x)$ \u3092\u6c42\u3081\u308b\u3068\uff0c<\/p>\n\n\n\n<p>$$f\\mskip 2mu\\prime (x)=3x^2+6x=3x(x+2)$$\u3067\u3059\u306d\u3002<\/p>\n\n\n\n<p>$f\\mskip 2mu\\prime (x)=0$ \u3068\u306a\u308b $x$ \u306f\uff0c$x=-2$\uff0c$0$ \u3067\u3042\u308a\uff0c$f\\mskip 2mu\\prime (x)$ \u306e\u7b26\u53f7\u306f\u6b21\u306e\u8868\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"271\" height=\"102\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5897\u6e1b\u88681.svg\" alt=\"\" class=\"wp-image-5475\"\/><noscript><img decoding=\"async\" width=\"271\" height=\"102\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5897\u6e1b\u88681.svg\" alt=\"\" class=\"wp-image-5475\"\/><\/noscript><\/figure>\n\n\n\n<p>\u3053\u306e\u8868\u306e\u3053\u3068\u3092\uff0c<span class=\"st-mymarker-s\">\u5897\u6e1b\u8868<\/span>\u3068\u3044\u3044\uff0c$\\nearrow$ \u3084 $\\searrow$ \u306f\u30b0\u30e9\u30d5\u304c\u5358\u8abf\u5897\u52a0\u304b\u5358\u8abf\u6e1b\u5c11\u304b\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u306a\u304a\uff0c$f\\mskip 2mu\\prime (x)$ \u306e\u7b26\u53f7\u304c\u308f\u304b\u308a\u306b\u304f\u3044\u5834\u5408\u306f\u56f3\u306e\u3088\u3046\u306b $y=f\\mskip 2mu\\prime (x)$ \u306e\u30b0\u30e9\u30d5\u3092\u8003\u3048\u3066\u307f\u308b\u3068\u3088\u3044\u3067\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"154\" height=\"125\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66374.svg\" alt=\"\" class=\"wp-image-5477\"\/><noscript><img decoding=\"async\" width=\"154\" height=\"125\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66374.svg\" alt=\"\" class=\"wp-image-5477\"\/><\/noscript><\/figure>\n\n\n\n<p>\u653e\u7269\u7dda\u306e $x$ \u5207\u7247\u304c $x=-2,\\,0$ \u3067\u3042\u308b\u3053\u3068\u3092\u8e0f\u307e\u3048\u308b\u3068\uff0c$x&lt;-2,\\,x&gt;0$ \u3067 $f\\mskip 2mu\\prime (x)&gt;0$\uff0c$f\\mskip 2mu\\prime (x)&gt;0$\uff0c$-2&lt;x&lt;0$ \u3067 $f\\mskip 2mu\\prime (x)&lt;0$ \u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u4ee5\u4e0a\u3092\u5229\u7528\u3057\u3066 $f(x)$ \u306e\u30b0\u30e9\u30d5\u3092\u304b\u304f\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"177\" height=\"178\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66156.svg\" alt=\"\" class=\"wp-image-5476\"\/><noscript><img decoding=\"async\" width=\"177\" height=\"178\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66156.svg\" alt=\"\" class=\"wp-image-5476\"\/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i-3\">\u95a2\u6570\u306e\u6975\u5927\u3068\u6975\u5c0f<\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6975\u5927\u30fb\u6975\u5c0f<\/h3>\n\n\n\n<p>$y=x^3+3x^2-2$ \u306b\u304a\u3044\u3066\uff0c$x=-2$ \u3092\u542b\u3080\u5341\u5206\u5c0f\u3055\u3044\u533a\u9593\u3067\u306f\uff0c$y$ \u306f $x=-2$ \u3067\u6700\u5927\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u540c\u69d8\u306b\uff0c$x=0$ \u3092\u542b\u3080\u5341\u5206\u5c0f\u3055\u3044\u533a\u9593\u3067\u306f\uff0c$y$ \u306f $x=0$ \u3067\u6700\u5c0f\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"96\" height=\"112\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66375.svg\" alt=\"\" class=\"wp-image-5479\"\/><noscript><img decoding=\"async\" width=\"96\" height=\"112\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u6570\u5b66375.svg\" alt=\"\" class=\"wp-image-5479\"\/><\/noscript><\/figure>\n\n\n\n<p>\u3053\u306e\u3068\u304d\uff0c$x=-2$ \u3067 $f(x)$ \u306f<span class=\"st-mymarker-s\">\u6975\u5927\u306b\u306a\u308b<\/span>\u3068\u3044\u3044\uff0c$f(-2)$ \u306e\u3053\u3068\u3092<span class=\"st-mymarker-s\">\u6975\u5927\u5024<\/span>\uff0c$x=0$ \u3067 $f(x)$ \u306f<span class=\"st-mymarker-s\">\u6975\u5c0f\u306b\u306a\u308b<\/span>\u3068\u3044\u3044\uff0c$f(0)$ \u306e\u3053\u3068\u3092<span class=\"st-mymarker-s\">\u6975\u5c0f\u5024<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305f\uff0c\u6975\u5927\u5024\u3068\u6975\u5c0f\u5024\u3092\u307e\u3068\u3081\u3066\uff0c<span class=\"st-mymarker-s\">\u6975\u5024<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>\u6975\u5927\u30fb\u6975\u5c0f<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$f(x)$ \u304c\u5fae\u5206\u53ef\u80fd\u306a\u95a2\u6570\u3067\u3042\u308b\u3068\u304d\uff0c$x=a$ \u306b\u304a\u3044\u3066\uff0c<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$\\begin{aligned}&amp;\\stext{$f\\mskip 2mu\\prime (x)$ \u306e\u7b26\u53f7\u304c\u6b63\u304b\u3089\u8ca0\u306b\u5909\u5316\u3059\u308b\u3068\u304d\uff0c$f(x)$ \u306f $x=a$ \u3067\u6975\u5927\u5024\u3092\u3068\u308b\u3002}\\\\&amp;\\stext{$f\\mskip 2mu\\prime (x)$ \u306e\u7b26\u53f7\u304c\u8ca0\u304b\u3089\u6b63\u306b\u5909\u5316\u3059\u308b\u3068\u304d\uff0c$f(x)$ \u306f $x=a$ \u3067\u6975\u5c0f\u5024\u3092\u3068\u308b\u3002}\\end{aligned}$$<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 \u63a5\u7dda\u3068\u6cd5\u7dda2 \u95a2\u6570\u306e\u5897\u6e1b3 \u95a2\u6570\u306e\u6975\u5927\u3068\u6975\u5c0f \u63a5\u7dda\u3068\u6cd5\u7dda \u63a5\u7dda \u95a2\u6570 $f(x)$ \u306e\u5fae\u5206\u4fc2\u6570 $f\\mskip 2mu\\prime (a)$ \u306f\uff0c\u66f2\u7dda $y=f(x)$ \u4e0a\u306e\u70b9 $(a,\\, &#8230; 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