将多项式f(x)=x3-x2 3按(x-1)的乘幂展开 确定函数f(x)=x3-x2-x+1的单调区间、凹凸区间、并...
1/(1-x)\u6cf0\u52d2\u5c55\u5f00\u5f0f \u8981\u8be6\u7ec6\u8fc7\u7a0b \u7b54\u6848\u662f1+x+x2+x3\u2026\u2026\u6cf0\u52d2\u516c\u5f0f\uff1af(x)=f(a)+f'(a)/1!*(x-a)+f''(a)/2!*(x-a)^2+...+f(n)(a)/n!*(x-a)^n\u73b0\u5728f(x)=1/(1-x)\uff0c\u6c42\u5bfc\u5f97\u5230f'(x)= -1/(1-x)^2 *(-1)=1/(1-x)^2\uff0cf''(x)= -2/(1-x)^3 *(-1)=2/(1-x)^3\uff0c\u4ee5\u6b64\u7c7b\u63a8\u5f97\u5230fn(x)=n! /(1-x)^(n+1)\u4ee3\u5165a=0\uff0c\u90a3\u4e48f(0)=1\uff0cf'(0)=1\uff0cfn(0)=n!\u6240\u4ee5\u89e3\u5f97f(x)=1+1!/1! *x+2!/2! *x^2+...+n!/n! *x^n
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*** \u697c\u4e0a \u4f60\u90a3\u6c42\u5bfc\u660e\u663e\u6c42\u9519\u4e86 f'(x)=3x^2-2x-1 ***
f(x)=(x-1)^2*(x+1) f'(x)=3x^2-2x-1=(x-1)(x+1/3)
\u5355\u8c03\u533a\u95f4\uff1a x=1\u65f6 \u5355\u8c03\u589e
-1/3<=x<=1\u65f6 \u5355\u8c03\u51cf
\u51f8\u51f9\u533a\u95f4\uff1a x=1\u65f6 \u51f9
-1<=x<=1\u65f6 \u51f8
\u6781\u9650 \uff1a \u65e0\u6781\u5927\u503c\u4e5f\u65e0\u6781\u5c0f\u503c
\u62d0\u70b9: \uff08-1/3,32/27\uff09 \uff081,0\uff09
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