若f'(cos^2x)=sin^2x,且f(0)= - 知识问答

若f'(cos^2x)=sin^2x,且f(0)=-(1/2),求方程f(x)=0的根

1个回答

f'(cos^2x)=sin^2x=1-cos^2x
f'(x)=1-x
f(x)=x-x^2/2+C
f(0)=C=-1/2
f(x)=x-x^2/2-1/2=0
x^2-2x+1=0
(x-1)^2=0
x=1

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