{"id":83,"date":"2011-11-26T23:04:56","date_gmt":"2011-11-26T14:04:56","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=83"},"modified":"2021-10-20T15:18:58","modified_gmt":"2021-10-20T06:18:58","slug":"ykr201101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201101\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2011\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(3\\) \u6b21\u95a2\u6570 \\(f(x) = x^3-3x^2-4x+k\\) \u306b\u3064\u3044\u3066, \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.\r\n\u305f\u3060\u3057, \\(k\\) \u306f\u5b9a\u6570\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(f(x)\\) \u304c\u6975\u5024\u3092\u3068\u308b\u3068\u304d\u306e \\(x\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u65b9\u7a0b\u5f0f \\(f(x)=0\\) \u304c\u7570\u306a\u308b \\(3\\) \u3064\u306e\u6574\u6570\u89e3\u3092\u3082\u3064\u3068\u304d, \\(k\\) \u306e\u5024\u304a\u3088\u3073\u305d\u306e\u6574\u6570\u89e3\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \\[\\begin{align}\r\nf'(x) & = 3x^2-6x-4 \\\\\r\n& = \\left( x-\\dfrac{3-\\sqrt{21}}{3} \\right) \\left( x-\\dfrac{3+\\sqrt{21}}{3} \\right)\r\n\\end{align}\\]\r\n\\(f'(x)=0\\) \u3092\u89e3\u304f\u3068\r\n\\[\r\nx = \\dfrac{3 \\pm \\sqrt{21}}{3}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x)\\) \u306e\u5897\u6e1b\u8868\u306f\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} x & \\cdots & \\dfrac{3 -\\sqrt{21}}{3} & \\cdots & \\dfrac{3 +\\sqrt{21}}{3} & \\cdots \\\\ \\hline\r\nf'(x) & + & 0 & - & 0 & + \\\\ \\hline f(x) & \\nearrow & \\text{\u6975\u5927} & \\searrow & \\text{\u6975\u5c0f} & \\nearrow \\end{array}\r\n\\]\r\n\u3088\u3063\u3066, \u6975\u5024\u3092\u3068\u308b\u306e\u306f\r\n\\[\r\nx = \\underline{\\dfrac{3 \\pm \\sqrt{21}}{3}}\r\n\\]\r\n

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

    \\(f(x)=0\\) \u304c \\(3\\) \u3064\u306e\u6574\u6570\u89e3\u3092\u3082\u3064\u306b\u306f, \\(\\dfrac{3 -\\sqrt{21}}{3} \\lt x \\lt \\dfrac{3 +\\sqrt{21}}{3}\\) \u306b \\(1\\) \u3064\u306e\u6574\u6570\u89e3\u3092\u3082\u3064\u5fc5\u8981\u304c\u3042\u308b.
    \r\n\\(4 \\lt \\sqrt{21} \\lt 5\\) \u306a\u306e\u3067, \u6574\u6570\u89e3\u306e\u5019\u88dc\u306f\r\n\\[\r\nx = 0 , 1 , 2\r\n\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(x = 0\\) \u304c\u89e3\u306e\u3068\u304d\r\n\\[\r\nf(0) = k = 0\r\n\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\nf(x) & = x^3-3x^2-4x \\\\\r\n& = x(x+1)(x-4)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u305d\u306e\u4ed6\u306e\u89e3\u306f, \\(x= -1 , 4\\) \u3067\u3068\u3082\u306b\u6574\u6570\u3067\u3042\u308b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(x = 1\\) \u304c\u89e3\u306e\u3068\u304d\r\n\\[\\begin{gather}\r\nf(1) = 1-3-4+k = k-6 = 0 \\\\\r\n\\text{\u2234} \\quad k = 6\r\n\\end{gather}\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\nf(x) & = x^3-3x^2-4x+6 \\\\\r\n& = (x-1)(x^2-2x-6)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u305d\u306e\u4ed6\u306e\u89e3\u306f, \\(x= 1 \\pm\\sqrt{7}\\) \u3067\u6574\u6570\u3067\u306a\u304f, \u4e0d\u9069.<\/p><\/li>\r\n

    3. 3*<\/strong>\u3000\\(x = 2\\) \u304c\u89e3\u306e\u3068\u304d\r\n\\[\\begin{gather}\r\nf(2) = 8-12-8+k = k-12 = 0 \\\\\r\n\\text{\u2234} \\quad k = 12\r\n\\end{gather}\\]\r\n\u3053\u306e\u3068\u304d,\r\n\\[\\begin{align}\r\nf(x) & = x^3-3x^2-4x+12 \\\\\r\n& = (x-2)(x+2)(x-3)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u305d\u306e\u4ed6\u306e\u89e3\u306f, \\(x= -2 , 3\\) \u3067\u3068\u3082\u306b\u6574\u6570\u3067\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      1*<\/strong> \uff5e 3*<\/strong> \u3088\u308a, \u6c42\u3081\u308b \\(k\\) \u306e\u5024\u3068\u6574\u6570\u89e3\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} k = 0 \\ \\text{\u306e\u3068\u304d} \\quad & x = -1 , 0 , 4 \\\\ k = 12\\ \\text{\u306e\u3068\u304d} \\quad & x = -2 , 2 , 3 \\end{array} \\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(3\\) \u6b21\u95a2\u6570 \\(f(x) = x^3-3x^2-4x+k\\) \u306b\u3064\u3044\u3066, \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \u305f\u3060\u3057, \\(k\\) \u306f\u5b9a\u6570\u3068\u3059\u308b. (1)\u3000\\(f(x)\\) \u304c\u6975\u5024\u3092\u3068\u308b\u3068\u304d\u306e \\(x\\) \u3092\u6c42\u3081\u3088. (2)\u3000\u65b9 … \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":[44],"tags":[13,9],"class_list":["post-83","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2011","tag-13","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/83","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=83"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/83\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=83"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=83"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=83"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}