已知函数f(x)满足f(x)=f'( 1 )e^(x- 1 )-f(0)x+( 1 /2)x² ( 1 )求f(x)解析式及单调区间
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已知函数f(x)满足f(x)=f'( 1 )e^(x- 1 )-f(0)x+( 1 /2)x² ( 1 )求f(x)解析式及单调区间
已知函数f(x)满足f(x)=f'( 1 )e^(x- 1 )-f(0)x+( 1 /2)x² ( 1 )求f(x)解析式及单调区间
已知函数f(x)满足f(x)=f'( 1 )e^(x- 1 )-f(0)x+( 1 /2)x² ( 1 )求f(x)解析式及单调区间
f(0)=f'(1)/e…………(1)
对f(x)求导:f'(x)=f'(1)e^(x-1)-f(0)+x
即:f'(1)=f'(1)-f(0)+1
得:f(0)=1
根据(1)有f'(1)=e
所以:f(x)=e^x-x+(1/2)x^2
f'(x)=e^x+x-1x>0,
f'(x)>0;
x
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