# Given the function # f(x) = 8 sqrt{ x} + 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,10] and find the c?

##### 1 Answer

Please see below.

#### Explanation:

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

A hypothesis is satisfied if it is true.

So we need to determine whether

It is.

(

and whether

It is.

(Remember that "differentiable" means the derivative exists.)

A very common way of stating the Mean Value Theorem gives the conclusion as:

There is a

A popular exercise (calculus and algebra) is to ask students to find the value or values of

To do this, find