{"id":1160,"date":"2015-07-11T22:55:13","date_gmt":"2015-07-11T13:55:13","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1160"},"modified":"2021-09-23T08:58:34","modified_gmt":"2021-09-22T23:58:34","slug":"thr201401","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201401\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2014\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(x = t +\\dfrac{1}{3t} \\ \\left( 0 \\lt t \\leqq \\dfrac{1}{2} \\right)\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(x\\) \u304c\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(x\\) \u306e\u65b9\u7a0b\u5f0f \\(x^2 +ax +b = 0\\) \u304c <strong>(1)<\/strong> \u306e\u7bc4\u56f2\u306b\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u306e\u89e3\u3092\u3082\u3064\u3088\u3046\u306a\u70b9 \\(( a , b )\\) \u306e\u5b58\u5728\u7bc4\u56f2\u3092\u56f3\u793a\u305b\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>\\(f(t) = t +\\dfrac{1}{3t} \\ \\left( 0 \\lt t \\leqq \\dfrac{1}{2} \\right)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nf'(t) & = 1 -\\dfrac{1}{3 t^2} \\\\\r\n& = \\dfrac{\\left( \\sqrt{3} -1 \\right) \\left( \\sqrt{3} +1 \\right)}{3 t^2} \\ .\r\n\\end{align}\\]\r\n\\(f'(t) = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\nt = \\dfrac{1}{\\sqrt{3}} \\ .\r\n\\]\r\n\\(\\displaystyle\\lim _ {t \\rightarrow +0} f(t) = \\infty\\) \u3067\u3042\u308b\u3053\u3068\u3082\u7528\u3044\u308c\u3070, \\(f(t)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccc} t & (0) & \\cdots & \\dfrac{1}{\\sqrt{3}} & \\cdots & \\dfrac{1}{2} \\\\ \\hline f'(t) & & - & 0 & + & \\\\ \\hline f(t) & ( \\infty ) & \\searrow & \\dfrac{2}{\\sqrt{3}} & \\nearrow & \\dfrac{7}{6} \\end{array}\r\n\\]\r\n\u305f\u3060\u3057\r\n\\[\\begin{align}\r\nf \\left( \\dfrac{1}{\\sqrt{3}} \\right) & = \\dfrac{1}{\\sqrt{3}} +\\dfrac{3}{\\sqrt{3}} = \\dfrac{2}{\\sqrt{3}} \\ , \\\\\r\nf \\left( \\dfrac{1}{2} \\right) & = \\dfrac{1}{2} +\\dfrac{2}{3} = \\dfrac{7}{6} \\ .\r\n\\end{align}\\]\r\n\u3092\u7528\u3044\u305f.<br \/>\r\n\u4ee5\u4e0a\u3088\u308a, \\(x\\) \u306e\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{x \\geqq \\dfrac{2}{\\sqrt{3}}} \\ .\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(g(x) = x^2 +ax +b\\) \u3068\u304a\u304f.<br \/>\r\n\u89e3\u306e\u500b\u6570\u306b\u5fdc\u3058\u3066, \u5834\u5408\u5206\u3051\u3057\u3066\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(1\\) \u3064\u306e\u89e3\u3092\u3082\u3064\u3068\u304d<br \/>\r\n\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\ng \\left( \\dfrac{2}{\\sqrt{3}} \\right) & = \\dfrac{4}{3} +\\dfrac{2a}{\\sqrt{3}} +b \\leqq 0 \\\\\r\n\\text{\u2234} \\quad b & \\leqq -\\dfrac{2a}{\\sqrt{3}} -\\dfrac{4}{3} \\ .\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(2\\) \u3064\u306e\u89e3\uff08\u91cd\u89e3\u3092\u542b\u3080\uff09\u3092\u3082\u3064\u3068\u304d<br \/>\r\n\u6b21\u306e \\(3\\) \u3064\u306e\u6761\u4ef6 [1] \uff5e [3] \u3092\u3059\u3079\u3066\u307f\u305f\u305b\u3070\u3088\u3044.\r\n<ul>\r\n<li><p>\\(g(x) = 0\\) \u306e\u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\nD = a^2 -4b & \\geqq 0 \\\\\r\n\\text{\u2234} \\quad b & \\leqq -\\dfrac{a^2}{4} \\quad ... [1] \\ .\r\n\\end{align}\\]<\/li>\r\n<li><p>\u653e\u7269\u7dda \\(y = g(x)\\) \u306e\u8ef8 \\(x = -\\dfrac{a}{2}\\) \u306e\u4f4d\u7f6e\u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n-\\dfrac{a}{2} & \\geqq \\dfrac{2}{\\sqrt{3}} \\\\\r\n\\text{\u2234} \\quad a & \\leqq -\\dfrac{4}{\\sqrt{3}} \\quad ... [2] \\ .\r\n\\end{align}\\]<\/li>\r\n<li><p>\\(g \\left( \\dfrac{2}{\\sqrt{3}} \\right)\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\ng \\left( \\dfrac{2}{\\sqrt{3}} \\right) & = \\dfrac{4}{3} +\\dfrac{2a}{\\sqrt{3}} +b \\geqq 0 \\\\\r\n\\text{\u2234} \\quad b & \\geqq -\\dfrac{2a}{\\sqrt{3}} -\\dfrac{4}{3} \\quad ... [3] \\ .\r\n\\end{align}\\]<\/li>\r\n<\/ul>\r\n<p><\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u3092\u542b\u3080\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/thr20140101.svg\" alt=\"thr20140101\" class=\"aligncenter size-full\" \/>\r\n<h2>\u3010 \u5225 \u89e3 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(f(t) = t +\\dfrac{1}{3t} \\ \\left( 0 \\lt t \\leqq \\dfrac{1}{2} \\right)\\) \u3068\u304a\u304f.\r\n\\[\r\n\\displaystyle\\lim _ {t \\rightarrow +0} f(t) = \\infty \\ .\r\n\\]\r\n\u307e\u305f, \u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\nf(t) \\geqq 2 \\sqrt{t \\cdot \\dfrac{1}{3t}} = \\dfrac{2}{\\sqrt{3}} \\ .\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f\r\n\\[\r\nt = \\dfrac{1}{3t} \\ \\text{\u3059\u306a\u308f\u3061} \\ t = \\dfrac{1}{\\sqrt{3}} \\ .\r\n\\]\r\n\u306e\u3068\u304d\u3067, \\(0 \\lt t \\leqq \\dfrac{1}{2}\\) \u306b\u542b\u307e\u308c\u3066\u3044\u308b.<br \/>\r\n\u3088\u3063\u3066\r\n\\[\r\n\\underline{x \\geqq \\dfrac{2}{\\sqrt{3}}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(x = t +\\dfrac{1}{3t} \\ \\left( 0 \\lt t \\leqq \\dfrac{1}{2} \\right)\\) \u3068\u3059\u308b. (1)\u3000\\(x\\) \u304c\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088. (2)\u3000\\(x\\) \u306e &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr201401\/\">\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":[118],"tags":[139,112],"class_list":["post-1160","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2014","tag-tokyo_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1160","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=1160"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1160\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}