# How do you verify whether rolle's theorem can be applied to the function #f(x)=x^3# in [1,3]?

##### 1 Answer

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?"

#### Explanation:

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

So we need to determine whether the hypotheses of 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** :

No, we do not have

Therefore we cannot apply Rolle's Theorem to