# How do you determine if rolles theorem can be applied to #f(x) = 2x^3 - x^2 - 8x + 4# on the interval [-2,2] and if so how do you find all the values of c in the interval for which f'(c)=0?

##### 1 Answer

Rolle's Theorem has three hypotheses:

**H1** :

**H2** :

**H3** :

In this question,

We can apply Rolle's Theorem if all 3 hypotheses are true.

So answer each question:

**H1** : Is

**H2** : Is

**H3** :

If the answer to all three questions is yes, then Rolle's can be applied to this function on this interval.

To solve

Select, as

(That is where Rolle's says there must be a solution. There may be more than one solution in the interval.)