Question1 point)
The graph below shows the total distance $s$, in miles, traveled by a bicyclist after $t$ hours. (a) Estimate the bicyclist's average velocity over the following time intervals.
Over $[0,1]$, the average velocity is approximately $15 \mathrm{mi} / \mathrm{hr}$. Over $[1,2.5]$, the average velocity is approximately $4 \mathrm{mi} / \mathrm{hr}$. Over $[2.5,3.5]$, the average velocity is approximately $18 \mathrm{mi} / \mathrm{hr}$. (b) Estimate the bicyclist's instantaneous velocity at the following times.
At $t=1 / 2$ hour, the instantaneous velocity is approximately $14 \mathrm{mi} / \mathrm{hr}$. At $t=2$ hours, the instantaneous velocity is approximately $10 \mathrm{mi} / \mathrm{hr}$. At $t=3$ hours, the instantaneous velocity is approximately $\square \mathrm{mi} / \mathrm{hr}$. (c) Estimate the bicyclist's maximum velocity and the specific time at which it occurs.
The maximum velocity is approximately $30 \mathrm{mi} / \mathrm{hr}$, which occurs when $t \approx 3 \mathrm{hr}$.
Note: You can earn partial credit on this problem.