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Unit 1 · Problem 1

apcalc-bc-u01-q01

3 points

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A cart has position s(t)=t²+3t meters. At t=2 seconds, find the average rate from 2 to 2+h (h≠0), then the instantaneous rate suggested by its limit.

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CriterionPoints
x1
Sets up the average rate as [s(2+h)−s(2)]/h[s(2+h)-s(2)]/h and obtains the position change 7h+h27h+h^2.
1
x2
Simplifies the average rate to 7+h7+h m/s for h≠0h\ne0.
1
x3
Calculates the instantaneous rate as 7 m/s by taking the limit of the average rate as h→0h\to0.
1

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