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

##### 1 Answer

#### Explanation:

First of all, let's remind that the Mean Value Theorem states that, if

id est, there exists an inner point in which the tangent line is parallel to the line connecting

Since your function is continuous in

Moreover, we can observe that

#f'(x) = 2/x# #f(b) = f(3) = 2ln(3)# #f(a) = f(1) = 2ln(1)=0# #b-a = 3-1 = 2#

So, we need to solve for

Inverting both sides, we have

And finally, multiplying by

We can also check that