# How do you determine if Rolles Theorem applies to the given function #x^3 - 9x# on [0,3]. If so, how do you find all numbers c on the interval that satisfy the theorem?

##### 1 Answer

Please see below.

#### Explanation:

When we are asked whether some theorem "applies" 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 Rolle's Theorem does apply to

**Extra**

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

To try to find the value(s) of

**conclusion of** Rolle's Theorem is