16. Let f(x) = x1/2 for x >= 0. With respect to the closed interval [1,4], what value of x satisfies the statement of the mean value theorem for derivatives?
|
A. 1 |
B. 3/2 |
C. 9/4 |
|
D. 3 |
E. 4 |
Solution: The answer is C
Since f(x) is continuous on the closed interval [1,4] and differentiable on the open interval (1,4), then by the mean value theorem there is a number x in (1,4) such that,
However, f’(x) is also given by,
By equating these two results, we can solve for x as follows:
