Chapter 13.1, Problem 20E

To determine

(a)

To show:

The inequality $-\frac{1}{2}\le g^{\prime }\left(x\right)\le \frac{1}{4}$ for all $x$ in $\left[1,2\right]$.

To determine

(b)

To show:

The inequality $\sqrt{2}\le g\left(x\right)\le \frac{3}{2}$ for all $x$ in $\left[1,2\right]$.