函数f(x)=x^2(x-1)^3,求f(x)极值点及极值,

问题描述:

函数f(x)=x^2(x-1)^3,求f(x)极值点及极值,

由f(x)=x²(x-1)³
=x²(x³-3x²+3x-1)
=x^5-3x^4+3x³-x²
f′(x)=5x^4-12x³+9x²-2x=0
x(x-1)(5x²-7x-2)=0
∴x=0,x=1
f(0)=0,f(1)=0