# Given the function #f(x)=(-x^2+9)/(4x)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,3] and find the c?

##### 2 Answers

The only hypothesis required by the mean value theorem is that

#### Explanation:

The only hypothesis required by the mean value theorem is that

As:

is in fact continuous in

We can calculate the definite integral as:

Then we can find

I will assume that you are referring to the Mean Value Theorem for Derivatives.

#### Explanation:

You determine whether it satisfies the hypotheses by determining whether

You find the

**Therefore this function satisfies the hypotheses of the Mean Value Theorem on this interval.**

To find

You should get