Chapter 4.4, Problem 82E

To determine

Whether the statement “If $f$ is continuous on $\left[a,b\right]$, $f$ is differentiable on $\left(a,b\right)$, and $f^{\prime }\left(x\right)>0$ for all $x$ in $\left(a,b\right)$, then the absolute minimum value of $f$ on $\left(a,b\right)$ is $f\left(a\right)$ or $f\left(b\right)$” is true or false.