{"id":263,"date":"2012-01-12T00:54:01","date_gmt":"2012-01-11T15:54:01","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=263"},"modified":"2021-03-24T08:36:12","modified_gmt":"2021-03-23T23:36:12","slug":"kyr200801","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200801\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592008\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\u76f4\u7dda \\(y=px+q\\) \u304c\u95a2\u6570 \\(y= \\log x\\) \u306e\u30b0\u30e9\u30d5\u3068\u5171\u6709\u70b9\u3092\u6301\u305f\u306a\u3044\u305f\u3081\u306b \\(p\\) \u3068 \\(q\\) \u304c\u6e80\u305f\u3059\u3079\u304d\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u6761\u4ef6\u3088\u308a, \\(x \\gt 0\\) \u3067\u3042\u308b.<br \/>\r\n\u4ee5\u4e0b\u306e\u7b49\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\\begin{align}\r\npx+q & = \\log x \\\\\r\n\\text{\u2234} \\quad px +q & -\\log x = 0\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x) =px +q -\\log x\\) \u306e\u30b0\u30e9\u30d5\u304c \\(x\\) \u8ef8\u3068\u5171\u6709\u70b9\u3092\u6301\u305f\u306a\u3044\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(p \\leqq 0\\) \u306e\u3068\u304d\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow +0} f(x) = \\infty , \\ \\displaystyle\\lim _ {x \\rightarrow \\infty} f(x) = -\\infty\r\n\\]\r\n\u306a\u306e\u3067, \u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u306e\u5171\u6709\u70b9\u3092\u3082\u3064.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(p \\gt 0\\) \u306e\u3068\u304d\r\n\\[\r\nf'(x) = p -\\dfrac{1}{x} = \\dfrac{px-1}{x}\r\n\\]\r\n\\(f'(x) =0\\) \u3092\u89e3\u304f\u3068\r\n\\[\r\nx = \\dfrac{1}{p}\r\n\\]\r\n\u307e\u305f\r\n\\[\r\n\\displaystyle\\lim _ {x \\rightarrow +0} f(x) = \\infty , \\ \\displaystyle\\lim _ {x \\rightarrow \\infty} f(x) = \\infty\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(x)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} x & (0) & \\cdots & \\dfrac{1}{p} & \\cdots & ( \\infty ) \\\\ \\hline f'(x) & & - & 0 & + & \\\\ \\hline f(x) & ( \\infty ) & \\searrow & q+1+\\log p & \\nearrow & ( \\infty ) \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\nf \\left( \\dfrac{1}{p} \\right) & = q+1+\\log p \\gt 0 \\\\\r\n\\text{\u2234} \\quad & p \\gt e^{-q-1}\r\n\\end{align}\\]\r\n\u3053\u308c\u306f \\(p \\gt 0\\) \u3082\u307f\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong>\u3088\u308a, \u6c42\u3081\u308b\u6761\u4ef6\u306f\r\n\\[\r\n\\underline{p \\gt e^{-q-1}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u76f4\u7dda \\(y=px+q\\) \u304c\u95a2\u6570 \\(y= \\log x\\) \u306e\u30b0\u30e9\u30d5\u3068\u5171\u6709\u70b9\u3092\u6301\u305f\u306a\u3044\u305f\u3081\u306b \\(p\\) \u3068 \\(q\\) \u304c\u6e80\u305f\u3059\u3079\u304d\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u3092\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":[49],"tags":[140,16],"class_list":["post-263","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2008","tag-kyoto_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/263","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=263"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/263\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=263"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=263"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}