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

##### 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 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** :

Therefore we can apply Rolle's Theorem to

To find the values of

So we need to solve

"By inspection

The graphing utility shows that there are 2 more solutions in the interval.

graph{sinx+xcosx [-4.384, 4.385, -2.19, 2.194]}