Question

If so, find the point(s) that are guaranteed to exist by the mean value theorem.

A) The points guaranteed by the mean value theorem are the critical points.
B) The points guaranteed by the mean value theorem are the maximum and minimum points.
C) The points guaranteed by the mean value theorem are the points where the derivative is zero.
D) The points guaranteed by the mean value theorem are somewhere between the endpoints.

Answer 1

The points guaranteed by the mean value theorem are the points where the derivative is zero, which are the critical points.

Step-by-step explanation:

The points guaranteed by the mean value theorem are the points where the derivative is zero. In other words, they are the critical points of the function. These points can be found by finding where the derivative of the function is equal to zero or undefined. The mean value theorem states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists at least one point where the derivative is equal to the average rate of change of the function over the closed interval.