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