{"id":1949,"date":"2021-11-03T16:15:17","date_gmt":"2021-11-03T07:15:17","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1949"},"modified":"2021-11-03T16:15:47","modified_gmt":"2021-11-03T07:15:47","slug":"htb201604","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201604\/","title":{"rendered":"\u4e00\u6a4b\u59272016\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(a\\) \u3092\u5b9f\u6570\u3068\u3057, \\(f(x) = x^3 -3ax\\) \u3068\u3059\u308b.\r\n\u533a\u9593 \\(-1\\leq x \\leqq 1\\) \u306b\u304a\u3051\u308b \\(| f(x) |\\) \u306e\u6700\u5927\u5024\u3092 \\(M\\) \u3068\u3059\u308b. \\(M\\) \u306e\u6700\u5c0f\u5024\u3068\u305d\u306e\u3068\u304d\u306e \\(a\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

\\[\r\n| f(-x) | = | -x^3 +3ax | = | x^3 -3ax | = | f(x) |\r\n\\]\r\n\u306a\u306e\u3067, \\(0 \\leqq x \\leqq 1\\) \u306b\u304a\u3051\u308b \\(| f(x) |\\) \u306e\u6700\u5927\u5024\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.\r\n\\[\r\nf'(x) = 3x^2 -3a = 3 \\left( x -\\sqrt{3} \\right) \\left( x +\\sqrt{3} \\right)\r\n\\]\r\n\u306a\u306e\u3067, \\(0 \\lt a \\lt 1\\) \u306e\u3068\u304d, \\(| f(x) |\\) \u306f\u6975\u5024\u3092\u3068\u308b.
\r\n\u3057\u305f\u304c\u3063\u3066, \\(M\\) \u306e\u5019\u88dc\u306f\r\n\\[\\begin{align}\r\n| f(0) | & = 0 \\\\\r\n| f(1) | & = | 1 -3a | = \\left\\{ \\begin{array}{ll} 1 -3a & \\left( \\ a \\lt \\dfrac{1}{3} \\ \\text{\u306e\u3068\u304d} \\ \\right) \\\\ 3a -1 & \\left( \\ a \\geqq \\dfrac{1}{3} \\ \\text{\u306e\u3068\u304d} \\ \\right) \\end{array} \\right. \\\\\r\n| f(a) | & = \\left| a \\sqrt{a} -3a \\sqrt{a} \\right| = 2 a^{\\frac{3}{2}} \\quad ( \\ 0 \\lt a \\lt 1 \\ \\text{\u306e\u3068\u304d} \\ )\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308b\u3068, \\(M\\) \u306e\u30b0\u30e9\u30d5\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n\"htb20160401\"\r\n

\u3088\u3063\u3066, \\(M\\) \u306f \\(a = \\underline{\\dfrac{1}{4}}\\) \u306e\u3068\u304d, \u6700\u5c0f\u5024 \\(\\underline{\\dfrac{1}{4}}\\) \u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092\u5b9f\u6570\u3068\u3057, \\(f(x) = x^3 -3ax\\) \u3068\u3059\u308b. \u533a\u9593 \\(-1\\leq x \\leqq 1\\) \u306b\u304a\u3051\u308b \\(| f(x) |\\) \u306e\u6700\u5927\u5024\u3092 \\(M\\) \u3068\u3059\u308b. \\(M\\) \u306e\u6700\u5c0f\u5024\u3068\u305d\u306e … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[161],"tags":[146,162],"class_list":["post-1949","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2016","tag-hitotsubashi","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1949","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=1949"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1949\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}