设f(x)=x^2e^(x-1)+ax^3+bx^ - 知识问答

设f(x)=x^2e^(x-1)+ax^3+bx^2已知x=-2和x=1为f(x)的极值点.求a和b的值

1个回答

f'(x)=[2x*e^(x-1)+x^2*e^(x-1)]+3ax^2+2bx
是极值点则f(-2)=f(1)=0
f(-2)=-4e^(-3)+4e^(-3)+12a-4b=0
3a-b=0
f(1)=2*e^0+e^0+3a+2b=0
3a+2b=-3
所以a=-1/3
b=-1

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