Chapter 14, Problem 1RE

The absolute maximum of a function always occurs where the derivative has a critical number.

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let $f\left(x\right)$ be a continuous function on the closed interval then the absolute extrema of $f\left(x\right)$ might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.