{"id":1203,"date":"2015-07-29T23:04:38","date_gmt":"2015-07-29T14:04:38","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1203"},"modified":"2021-10-30T20:12:18","modified_gmt":"2021-10-30T11:12:18","slug":"tkb201401","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201401\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2014\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(t\\) \u3092\u5b9f\u6570\u306e\u5b9a\u6570\u3068\u3059\u308b. \u5b9f\u6570\u5168\u4f53\u3092\u5b9a\u7fa9\u57df\u3068\u3059\u308b\u95a2\u6570 \\(f(x)\\) \u3092\r\n\\[\r\nf(x) = -2x^2 +8tx -12x +t^3 -17t^2 +39t -18\r\n\\]\r\n\u3068\u5b9a\u3081\u308b. \u3053\u306e\u3068\u304d, \u95a2\u6570 \\(f(x)\\) \u306e\u6700\u5927\u5024\u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000(1)<\/strong> \u306e\u300c\u95a2\u6570 \\(f(x)\\) \u306e\u6700\u5927\u5024\u300d\u3092 \\(g(t)\\) \u3068\u3059\u308b. \\(t\\) \u304c \\(t \\geqq -\\dfrac{1}{\\sqrt{2}}\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(g(t)\\) \u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    (1)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\nf(x) & = -2 \\left\\{ x -(2t-3) \\right\\}^2 +2 (2t-3)^2 \\\\\r\n& \\qquad +t^3 -17t^2 +39t -18 \\\\\r\n& = -2 \\left\\{ x -(2t-3) \\right\\}^2 +t^3 -9 t^2 +15t\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{t^3 -9 t^2 +15t}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\ng'(t) & = 3t^2 -18t +15 \\\\\r\n& = 3 (t-1) (t-5)\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(g(t)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|cccccc} x & -\\dfrac{1}{\\sqrt{2}} & \\cdots & 1 & \\cdots & 5 & \\cdots \\\\ \\hline g'(t) & & + & 0 & - & 0 & + \\\\ \\hline g(t) & & \\nearrow & \\text{\u6975\u5927} & \\searrow & \\text{\u6975\u5c0f} & \\nearrow \\end{array}\r\n\\]\r\n\u3053\u3053\u3067 \\(g(5) = g(-1)\\) , \\(-1 \\lt -\\dfrac{1}{\\sqrt{2}} \\lt 1\\) \u306a\u306e\u3067\r\n\\[\r\ng \\left( -\\dfrac{1}{\\sqrt{2}} \\right) \\gt g(5)\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\ng(5) = \\underline{-25}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\\(t\\) \u3092\u5b9f\u6570\u306e\u5b9a\u6570\u3068\u3059\u308b. \u5b9f\u6570\u5168\u4f53\u3092\u5b9a\u7fa9\u57df\u3068\u3059\u308b\u95a2\u6570 \\(f(x)\\) \u3092 \\[ f(x) = -2x^2 +8tx -12x +t^3 -17t^2 +39t -18 \\] \u3068\u5b9a\u3081 … \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":[123],"tags":[149,112],"class_list":["post-1203","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2014","tag-tokyo_b","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1203","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=1203"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1203\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}