# Given the function #f(x)=-(6x+24)^(2/3)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-4,-1] and find the c?

##### 1 Answer

See below.

#### Explanation:

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

In this question,

We can apply the Mean Value Theorem if both hypotheses are true.

This function is continuous on its domain,

So

Therefore

So we know that there is a

To find the

to get