Question

Determine whether Rolle's Theorem can be applied to f(x)= (x-3)(x+1)^2on [-1,3]. If so, find the values of c whose existence is guaranteed by the theorem

Answer 1

Rolle's theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero.

Answer 2

using that you could probably figure this out :)