f(x)的导数f'(x)=3x^2-2(a+1)x+a-2,且f(0)=2a,求不等式f(x)

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f(x)的导数f'(x)=3x^2-2(a+1)x+a-2,且f(0)=2a,求不等式f(x)
f(x)的导数f'(x)=3x^2-2(a+1)x+a-2,且f(0)=2a,求不等式f(x)

f(x)的导数f'(x)=3x^2-2(a+1)x+a-2,且f(0)=2a,求不等式f(x)
f(x)=x^3-(a+1)x^2+(a-2)x+2a,取x=-1,f(-1)=0,故f(x)=(x+1)(x^2-(a+2)x+2a)(竖式除法),x^2-(a+2)x+2a=(x-2)(x-a)(十字相乘法),所以f(x)=(x+1)(x-2)(x-a)
(1)a