Chapter 3.1, Problem 67E

To determine

We need to plot the graph of $f\left(x\right)=x^{5/2}$ on $\left[0,6\right]$

(a) We need to justify the inequalities for $h>0$

$\frac{f\left(4-h\right)-f\left(4\right)}{h}\le f^{\text{'}}\left(4\right)\le \frac{f\left(4+h\right)-f\left(4\right)}{h}$

(b) We need to compute $f^{\text{'}}\left(4\right)$

(c) We need to plot $y=f\left(x\right)$ and the tangent line at $x=4$