# How do you determine if rolles theorem can be applied to #sqrt(x) - 1/5x # on the interval [0,25] 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.

**H1** : This function is continuous on its domain,

**H2** :

So

**H3** :

Therefore we can apply Rolle's Theorem to

.

As an algebra exercise you've also been asked to actually **find** the values of

To do that, find