Question

Determine whether Rolle's Theorem can be applied to the function f(x)=(x+3)(x-2)^2 on the closed interval [-3,2]. If Rolle's Theorem can be applied, find all numbers c in the open interval (-3,2) such that f (prime)©=0

Answer 1

Rolle's Theorem states that if a function has two distinct points, a and b, with the same value, there must be at least one point c on the closed interval [a,b] such that f'(c)=0.

Basically, Rolle's Theorem can be applied if f(-3)=f(2).

To solve this problem you need to do two things:

1. Evaluate f(-3) and f(2) and determine if f(-3)=f(2).

2. If f(-3)=f(2), derive f(x) and solve f'(c)=0.