The derivative of a function isf'(x)= (x-1)²(x+3).

Find the value of x at each point wherefhas a

(a) local maximum

(b) local minimum

(c) point of inflection

I got that the maximum is at x=-3, and minimum at x=1. I got x=-5/3 and x=1 as points of inflection.

Can anyone tell me if I'm right, please?