{"id":683,"date":"2013-03-12T21:53:47","date_gmt":"2013-03-12T12:53:47","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=683"},"modified":"2021-09-16T07:05:32","modified_gmt":"2021-09-15T22:05:32","slug":"ngr200702","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr200702\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2007\uff1a\u7b2c2\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u95a2\u6570 \\(f(x) = 2x^3-3x^2+1\\) \u306e\u30b0\u30e9\u30d5\u3092\u304b\u3051.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u65b9\u7a0b\u5f0f \\(f(x) = a\\) \uff08 \\(a\\) \u306f\u5b9f\u6570\uff09\u304c\u76f8\u7570\u306a\u308b \\(3\\) \u3064\u306e\u5b9f\u6570\u89e3 \\(\\alpha \\lt \\beta \\lt \\gamma\\) \u3092\u6301\u3064\u3068\u3059\u308b. \\(\\ell = \\gamma -\\alpha\\) \u3092 \\(\\beta\\) \u306e\u307f\u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<li><p><strong>(3)<\/strong>\u3000<strong>(2)<\/strong> \u306e\u6761\u4ef6\u306e\u3082\u3068\u3067\u5909\u5316\u3059\u308b\u3068\u304d \\(\\ell\\) \u306e\u52d5\u304f\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\[\r\nf'(x) = 6x^2 -6x = 6x(x-1) \\ .\r\n\\]\r\n\\(f'(x)=0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\nx = 0 , 1 \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} x & \\cdots & 0 & \\cdots & 1 & \\cdots \\\\ \\hline f'(x) & + & 0 & - & 0 & + \\\\ \\hline f(x) & \\nearrow & 1 & \\searrow & 0 & \\nearrow \\end{array} \\ .\r\n\\]\r\n\u3088\u3063\u3066, \\(y = f(x)\\) \u306e\u30b0\u30e9\u30d5\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/nagoya_r_2007_02_01.png\" alt=\"nagoya_r_2007_02_01\" class=\"aligncenter size-full\" \/>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(y = f(x)\\) \u306e\u30b0\u30e9\u30d5\u306e\u5f62\u304b\u3089, \\(f(x) = a\\) \u304c\u76f8\u7570\u306a\u308b \\(3\\) \u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u306e\u306f\r\n\\[\r\n0 \\lt a \\lt 1 \\quad ... [1] \\ .\r\n\\]\r\n\u306e\u7bc4\u56f2\u3067\u3042\u308a\r\n\\[\r\n-\\dfrac{1}{2} \\lt \\alpha \\lt 0 \\lt \\beta \\lt 1 \\lt \\gamma \\lt \\dfrac{3}{2} \\quad ... [2] \\ .\r\n\\]\r\n\\(f(x)= a\\) \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\n2x^3 -3x^2 -a+1 = 0 \\ .\r\n\\]\r\n\u306a\u306e\u3067, \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\\begin{align}\r\n\\alpha +\\beta +\\gamma & = \\dfrac{3}{2} \\quad ... [3] , \\\\\r\n\\alpha \\beta +\\beta \\gamma +\\gamma \\alpha & = 0 \\quad ... [4] \\ .\r\n\\end{align}\\]\r\n[3] \u3088\u308a\r\n\\[\r\n\\alpha +\\gamma = \\dfrac{3}{2} -\\beta \\ .\r\n\\]\r\n\u3053\u308c\u3092 [4] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\alpha \\gamma & +\\beta \\left( \\dfrac{3}{2} -\\beta \\right) = 0 \\\\\r\n\\text{\u2234} \\quad \\alpha \\gamma & = -\\beta \\left( \\dfrac{3}{2} -\\beta \\right) \\ .\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\ell & = \\sqrt{( \\alpha +\\gamma )^2 -4 \\alpha \\gamma} \\\\\r\n& = \\sqrt{\\left( \\dfrac{3}{2} -\\beta \\right)^2 +4 \\beta \\left( \\dfrac{3}{2} -\\beta \\right)} \\\\\r\n& = \\sqrt{-3 \\beta^2 +3 \\beta +\\dfrac{9}{4}} \\\\\r\n& = \\underline{\\dfrac{1}{2} \\sqrt{3 ( 3+ 4 \\beta -4 \\beta^2 )}} \\ .\r\n\\end{align}\\]\r\n<p><strong>(3)<\/strong><\/p>\r\n[2] \u3088\u308a, \\(0 \\lt \\beta \\lt 1\\) \u3067\u3042\u308a\r\n\\[\r\n\\ell = \\sqrt{-3 \\left( \\beta -\\dfrac{1}{2} \\right)^2 +3} \\ .\r\n\\]\r\n\u306a\u306e\u3067, \\(\\ell\\) \u306e\u53d6\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{\\dfrac{3}{2} \\lt \\ell \\leqq \\sqrt{3}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\u95a2\u6570 \\(f(x) = 2x^3-3x^2+1\\) \u306e\u30b0\u30e9\u30d5\u3092\u304b\u3051. (2)\u3000\u65b9\u7a0b\u5f0f \\(f(x) = a\\) \uff08 \\(a\\) \u306f\u5b9f\u6570\uff09\u304c\u76f8\u7570\u306a\u308b \\(3\\) \u3064\u306e\u5b9f\u6570\u89e3 \\(\\alpha \\lt \\beta \\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ngr200702\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[97],"tags":[143,109],"class_list":["post-683","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2007","tag-nagoya_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/683","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=683"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/683\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=683"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=683"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}