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Problem 21

The accompanying graph shows the total distance s traveled by a bicyclist after $t$ hours.
a. Estimate the bicyclist's average speed over the time intervals $[0,1],[1,2.5],$ and $[2.5,3.5] .$
b. Estimate the bicyclist's instantaneous speed at the times $t=\frac{1}{2}$ , $t=2,$ and $t=3 .$
c. Estimate the bicyclist's maximum speed and the specific time at which it occurs.

a) $15 \mathrm{mph}, 3.3 \mathrm{mph}, 10 \mathrm{mph}$
b) $15 \mathrm{mph}, 0 \mathrm{mph}, 4 \mathrm{mph}$
c) $20 \mathrm{mph}$ at $\mathrm{t}=3.5$

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