Chapter 11.7, Problem 75E

Work the following exercises.

On-the-Job Training Studies show that after t hours on the job, the number of items a supermarket cashier can scan per minute is given by

$F\left(t\right)=60-\frac{150}{\sqrt{8+t^2}}.$

Find $F^{\prime }\left(t\right)$, the rate at which the cashier's speed is increasing.

Find $F^{\prime }\left(5\right)$.

Find $F^{\prime }\left(40\right)$.

Is the cashier's speed increasing more rapidly after 5 hours or after 40 hours?