Chapter 4, Problem 53RE

In each part, determine whether the statement is true or false, and justify your answer.

(a) If $f$ is differentiable on the open interval $\left(a,b\right),$ and if $f$ has an absolute extremum on that interval, then it must occur at a stationary point of $f$ .

(b) If $f$ is continuous on the open interval $\left(a,b\right),$ and if $f$ has an absolute extremum on that interval, then it must occur at a stationary point of $f$ .