# How do you determine whether Rolle’s Theorem can be applied to #f(x)=x(x-6)^2# on the interval [0,6]?

##### 1 Answer

See the explanation section.

#### Explanation:

When we are asked whether some theorem "can be applied" to some situation, we are really being asked "Are the hypotheses of the theorem true for this situation?"

(The hypotheses are also called the antecedent, of 'the if parts'.)

So we need to determine whether the hypotheses ot Rolle's Theorem are true for the function

Rolle's Theorem has three hypotheses:

**H1** :

**H2** :

**H3** :

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

**H1** : The function

**H2** : The function

[Because the derivative,

**H3** :

Therefore we can apply Rolle's Theorem to

**Extra**

Because the hypotheses are true, we know without further work, that the conclusion of Rolle's Theorem. That is, we know that there is a

Sometimes, as an equation solving exercise, students are asked to find the

In this question,