Chapter 4.1, Problem 87E

(a)

To determine

To find: The function travel time T as a function of x, where $0\le x\le 50$.

(b)

To determine

To find: The critical points of the function $T=\frac{\sqrt{2500+x^2}}{2}+\frac{50-x}{4}$ on $\left(0,50\right)$.

(c)

To determine

To evaluate: T at the critical point and at the endpoints ( $x=0$ and $x=50$) and verify that the critical points corresponds to the absolute minimum; find the minimum travel time.

(c)

To determine

To draw: The graph of the function $T=\frac{\sqrt{2500+x^2}}{2}+\frac{50-x}{4}$, to confirm the results obtained.