Chapter 3.1, Problem 69E

(a)

To determine

To graph: $f(x)\text{and}f\text{'}(x)$ in the window $\left[0,6\right]\text{by}\left[-5,20\right]$, where $f(x)=\frac{160x^{-0.4}+94.8}{4x^{-0.4}+15.8}$ $\left(0\le x\le 37\right)$ represents the area of the pupil in square millimeters, where $x$ units of light are entering the eye per unit time.

(b)

To determine

The size of the pupil when $3$ units of light are entering the eye per unit time.

(c)

To determine

The intensity of light for which the pupil size is $11{\text{mm}}^{\text{2}}$

(d)

To determine

The rate of change of the pupil with respect to a unit change in light intensity, when $3$ units of light are entering per unit time.