函数y等于sin平方x在[π/(-2),π/2]上满足罗尔定理§等于多少？ 验证函数f(x)=sinx在[0,兀]上满足罗尔定理的条件
\u51fd\u6570f(x)=sin05x\u5728\u533a\u95f4[0,\u03c0]\u4e0a( )\u7f57\u5c14\u5b9a\u7406\u5f53\u7136\u662f\u6ee1\u8db3\u7f57\u5c14\u5b9a\u7406\u7684
y=sin²x\uff0c\u5373x=0\uff0cx=\u03c0\u65f6y=0
\u663e\u7136y'=2sinx *cosx=sin2x
\u90a3\u4e48\u5728\u533a\u95f4[0,\u03c0]\u4e0a\uff0cx=\u03c0/2\u65f6
y'=sin\u03c0=0
f(x)=sinx[0,\u03c0]\u4e0a\u8fde\u7eed\uff0c\u5728(0,\u03c0)\u4e0a\u53ef\u5bfc
\u4e14f(0)=sin0=0,f(\u03c0)=sin\u03c0=0
\u5373f(0)=f(\u03c0)
\u6240\u4ee5f(x)=sinx\u5728[0,\u03c0]\u4e0a\u6ee1\u8db3\u7f57\u5c14\u5b9a\u7406\u6761\u4ef6.
\u5e0c\u671b\u80fd\u5e2e\u5230\u4f60\uff01
(sin^2 x)' = 2sin x cos x = sin 2x = (1-1)/π = 0
x = 0, y = 0 点的切线的斜率 = 0.
绛旓細sin^2 蟺/(-2) = sin^2 蟺/2 = 1 (sin^2 x)' = 2sin x cos x = sin 2x = (1-1)/蟺 = 0 x = 0, y = 0 鐐圭殑鍒囩嚎鐨勬枩鐜 = 0.
绛旓細f(x)=y=sin²x=(1-cos2x)/2=-1/2*cos2x+1/2 鏈灏忔鍛ㄦ湡T=2蟺/2=蟺 f(-x)=-1/2*cos(-2x)+1/2=-1/2*cos2x+1/2=f(x)锛屾墍浠ユ槸鍋跺嚱鏁
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
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