{"id":1965,"date":"2021-11-14T09:50:54","date_gmt":"2021-11-14T00:50:54","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1965"},"modified":"2021-11-14T09:50:54","modified_gmt":"2021-11-14T00:50:54","slug":"tkr202105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr202105\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2021\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(\\alpha\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b.\r\n\\(0 \\leqq \\theta \\leqq \\pi\\) \u306b\u304a\u3051\u308b \\(\\theta\\) \u306e\u95a2\u6570 \\(f( \\theta )\\) \u3092,\r\n\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\(( -\\alpha , -3 )\\) , P \\(( \\theta +\\sin \\theta , \\cos \\theta )\\) \u9593\u306e\u8ddd\u96e2 AP \u306e \\(2\\) \u4e57\u3068\u3057\u3066\u5b9a\u3081\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(0 \\lt \\theta \\lt \\pi\\) \u306e\u7bc4\u56f2\u306b \\(f'( \\theta ) = 0\\) \u3068\u306a\u308b \\(\\theta\\) \u304c\u305f\u3060 \\(1\\) \u3064\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306a \\(\\alpha\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p>\r\n

      \r\n
    1. \\(0 \\leqq \\theta \\leqq \\pi\\) \u306b\u304a\u3051\u308b \\(\\theta\\) \u306e\u95a2\u6570 \\(f( \\theta )\\) \u306f, \u533a\u9593 \\(0 \\lt \\theta \\lt \\dfrac{\\pi}{2}\\) \u306e\u3042\u308b\u70b9\u306b\u304a\u3044\u3066\u6700\u5927\u306b\u306a\u308b.<\/li>\r\n<\/ol><\/li>\r\n<\/ol>\r\n
      \r\n\r\n

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

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

      \u6761\u4ef6\u3088\u308a\r\n\\[\r\nf( \\theta ) = ( \\theta +\\sin \\theta +\\alpha )^2 +( \\cos \\theta +3 )^2\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nf'( \\theta ) & = 2 ( \\theta +\\sin \\theta +\\alpha ) ( 1 +\\cos \\theta ) -2 ( \\cos \\theta +3 ) \\sin \\theta \\\\\r\n& = 2 ( \\theta +\\alpha ) ( \\cos \\theta +1 ) +2 \\sin \\theta -6 \\sin \\theta \\\\\r\n& = 2 \\underline{\\left\\{ ( \\theta +\\alpha ) ( \\cos \\theta +1 ) -2 \\sin \\theta \\right\\}} _ {[1]}\r\n\\end{align}\\]\r\n[1] \u3092 \\(g( \\theta )\\) \u3068\u304a\u3044\u3066\r\n\\[\\begin{align}\r\ng'( \\theta ) & = \\cos \\theta +1 -( \\theta +\\alpha ) \\sin \\theta -2 \\cos \\theta \\\\\r\n& = -( \\theta +\\alpha ) \\sin \\theta -\\cos \\theta +1 \\ , \\\\\r\ng''( \\theta ) & = -\\sin \\theta -( \\theta +\\alpha ) \\cos \\theta +\\sin \\theta \\\\\r\n& = -( \\theta +\\alpha ) \\cos \\theta\r\n\\end{align}\\]\r\n\\(g''( \\theta ) = 0\\) \u3092\u3068\u304f\u3068, \\(\\theta +\\alpha \\gt 0\\) \u306a\u306e\u3067, \\(\\theta = \\dfrac{\\pi}{2}\\) .
      \r\n\u3057\u305f\u304c\u3063\u3066, \\(g'( \\theta )\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u901a\u308a.\r\n\\[\r\n\\begin{array}{c|ccccc} \\theta & 0 & \\cdots & \\dfrac{\\pi}{2} & \\cdots & \\pi \\\\ \\hline g''( \\theta ) & & - & 0 & + & \\\\ \\hline g'( \\theta ) & 0 & \\searrow & \\text{\u6700\u5c0f} & \\nearrow & 2 \\end{array}\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\r\ng' \\left( \\dfrac{\\pi}{2} \\right) = 1 -\\dfrac{\\pi}{2} -\\alpha \\lt 0\r\n\\]\r\n\u306a\u306e\u3067, \\(g'( \\theta ) = 0\\) \u306f \\(\\dfrac{\\pi}{2} \\lt \\theta \\lt \\pi\\) \u306b\u89e3 \\(\\beta\\) \u304c \\(1\\) \u3064\u5b58\u5728\u3059\u308b.
      \r\n\\(g( \\theta )\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u901a\u308a.\r\n\\[\r\n\\begin{array}{c|ccccc} \\theta & 0 & \\cdots & \\beta & \\cdots & \\pi \\\\ \\hline g'( \\theta ) & & - & 0 & + & \\\\ \\hline g( \\theta ) & 2 \\alpha & \\searrow& \\text{\u6700\u5c0f} & \\nearrow & 0 \\end{array}\r\n\\]\r\n\u3053\u3053\u3067\r\n\\[\r\ng( \\beta ) \\lt g( \\pi ) = 0\r\n\\]\r\n\u306a\u306e\u3067, \\(g( \\theta ) = 0\\) \u306f \\(0 \\lt \\theta \\lt \\beta\\) \u306b\u89e3 \\(\\gamma\\) \u304c \\(1\\) \u3064\u5b58\u5728\u3059\u308b.
      \r\n\u3088\u3063\u3066, \\(\\gamma\\) \u306f \\(f'( \\theta ) = 0\\) \u306e\u305f\u3060 \\(1\\) \u3064\u306e\u89e3\u3068\u306a\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

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

      (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070, \\(f( \\theta )\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u901a\u308a.\r\n\\[\r\n\\begin{array}{c|ccccc} \\theta & 0 & \\cdots & \\gamma & \\cdots & \\pi \\\\ \\hline f'( \\theta ) & & + & 0 & - & \\\\ \\hline f( \\theta ) & & \\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\theta = \\gamma\\) \u3067 \\(f( \\theta )\\) \u306f\u6700\u5927\u3068\u306a\u308b.
      \r\n\\(f'( \\theta )\\) \u306e\u5897\u6e1b\u306b\u7740\u76ee\u3059\u308c\u3070, \\(0 \\lt \\gamma \\lt \\dfrac{\\pi}{2}\\) \u3068\u306a\u308b\u6761\u4ef6\u3092\u8003\u3048\u308c\u3070\u3088\u304f\r\n\\[\\begin{align}\r\nf' \\left( \\dfrac{\\pi}{2} \\right) & = 2 \\left( \\dfrac{\\pi}{2} +\\alpha -2 \\right) \\lt 0 \\\\\r\n\\text{\u2234} \\quad & \\underline{0 \\lt \\alpha \\lt 2 -\\dfrac{\\pi}{2}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\alpha\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \\(0 \\leqq \\theta \\leqq \\pi\\) \u306b\u304a\u3051\u308b \\(\\theta\\) \u306e\u95a2\u6570 \\(f( \\theta )\\) \u3092, \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 A \\(( … \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":[164],"tags":[139,165],"class_list":["post-1965","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2021","tag-tokyo_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1965","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=1965"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1965\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}