# How do you verify that the function #f(x) = (x)/(x+2)# satisfies the hypotheses of the Mean Value Theorem on the given interval [1,4], then find all numbers c that satisfy the conclusion of the Mean Value Theorem?

##### 1 Answer

The mean value theorem requires a function to be continuous in a closed interval

These conditions are easily checked, since the only point in which the function is not defined is

As for the derivative, using the ratio formula

we have that

Now that we ensured ouselves to be in the right hypothesis, we must find a point

We know that

Isolating the terms involving

Since

As you can see in this link, the derivative evaluated in that point equals to