{"id":723,"date":"2013-04-10T21:37:39","date_gmt":"2013-04-10T12:37:39","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=723"},"modified":"2021-11-04T16:06:54","modified_gmt":"2021-11-04T07:06:54","slug":"htb200704","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200704\/","title":{"rendered":"\u4e00\u6a4b\u59272007\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(a\\) \u3092\u5b9a\u6570\u3068\u3057, \\(f(x) = x^3-3ax^2+a\\) \u3068\u3059\u308b.\r\n\\(x \\leqq 2\\) \u306e\u7bc4\u56f2\u3067 \\(f(x)\\) \u306e\u6700\u5927\u5024\u304c \\(105\\) \u3068\u306a\u308b\u3088\u3046\u306a \\(a\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\\[\r\nf'(x) = 3x^2 -6ax = 3x(x-2a)\r\n\\]\r\n\\(f'(x)=0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\nx=0 , 2a\r\n\\]\r\n\u6975\u5927\u3068\u3068\u306a\u308b\u70b9\u306b\u3082\u7740\u76ee\u3059\u308c\u3070, \\(x \\leqq 2\\) \u306b\u304a\u3044\u3066\u6700\u5927\u5024\u3068\u306a\u308b\u5019\u88dc\u306f\r\n\\[\\begin{align}\r\nf(2) & = 8-12a+a = 8-11a , \\\\\r\nf(2a) & = 8a^3 -12a^3 +a = -4a^3+a \\quad ( \\ a \\lt 0 \\text{\u306e\u3068\u304d\u306e\u307f} ) , \\\\\r\nf(0) & = a \\quad ( \\ a \\gt 0 \\text{\u306e\u3068\u304d\u306e\u307f} )\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308b\u3068, \u4e0b\u306e\u30b0\u30e9\u30d5\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/hitotsubashi_2007_04_01.png\" alt=\"hitotsubashi_2007_04_01\" class=\"aligncenter size-full\" \/>\r\n<p>\u3088\u3063\u3066, \\(f(x)\\) \u306e \\(x \\leqq 2\\) \u306b\u304a\u3051\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\left\\{\\begin{array}{ll} -4a^3+a & ( \\ a \\lt -2 \\text{\u306e\u3068\u304d} ) \\\\ 8-11a & \\left( \\ -2 \\leqq a \\lt \\dfrac{2}{3} \\text{\u306e\u3068\u304d} \\right) \\\\ a & \\left( \\ a\\geq \\dfrac{2}{3} \\text{\u306e\u3068\u304d} \\right) \\end{array}\\right.\r\n\\]\r\n\u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b\u3064\u3044\u3066, \u6700\u5927\u5024\u304c \\(105\\) \u306b\u306a\u308b\u3068\u304d\u3092\u8abf\u3079\u308b\u3068<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(a \\lt -2\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n-4a^3+a & = 105 \\\\\r\n(a+3)(4a^2 -12a +35) & = 0 \\\\\r\n\\text{\u2234} \\quad a = -3 &\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(a \\lt -2\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(-2 \\leqq a \\lt \\dfrac{2}{3}\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n8-11a & = 105 \\\\\r\n\\text{\u2234} \\quad a & = -\\dfrac{97}{11}\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(-2 \\leqq a \\lt \\dfrac{2}{3}\\) \u3092\u6e80\u305f\u3055\u305a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(a \\geqq \\dfrac{2}{3}\\) \u306e\u3068\u304d\r\n\\[\r\na = 105\r\n\\]\r\n\u3053\u308c\u306f \\(a \\geqq \\dfrac{2}{3}\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b \\(a\\) \u306e\u5024\u306f\r\n\\[\r\na = \\underline{-3 , 105}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u5b9a\u6570\u3068\u3057, \\(f(x) = x^3-3ax^2+a\\) \u3068\u3059\u308b. \\(x \\leqq 2\\) \u306e\u7bc4\u56f2\u3067 \\(f(x)\\) \u306e\u6700\u5927\u5024\u304c \\(105\\) \u3068\u306a\u308b\u3088\u3046\u306a \\(a\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.","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":[107],"tags":[146,109],"class_list":["post-723","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2007","tag-hitotsubashi","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/723","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=723"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/723\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=723"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=723"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=723"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}