# How do you determine whether the function #f(x) = abs(x-3)# satisfies the hypotheses of the mean value theorem on the indicated interval (a,b), and if so how do you find all numbers c on [0,4] ?

##### 1 Answer

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

In this question,

We can apply the Mean Value Theorem if both hypotheses are tru

This function is continuous on its domain,

Now,

So, for the derivative, we have:

So

This function does not satisfy the hypotheses on

**In addition** , since the derivative is always

and

There is no

(There is no