Question

求下列函数的极值 f(x)=(x-3)²(x-2)

Answer 1

令f(x)=y

f'(x)=2(x-3)(x-2)+(x-3)²

=(x-3)(2(x-2)+(x-3))

=(x-3)(3x-7)

若f'(x)=0,则x=3或x=7/3

x0,则x=3时,f(x)取极小值

f(3)=0

则y极小值为x=3时,y=0

极大值为x=7/3时,y=4/27