AP Calculus BC 2.1 Defining Average and Instantaneous Rates of Change At a Point Questions

Practice AP Calculus BC questions on calculating average rates and connecting them with instantaneous rate of change at a point.

Covered syllabus points

CHA-2.A—Determine average rates of change using difference quotients CHA-2.B—Represent the derivative of a function as the limit of a difference quotient

[Maximum number: 1]

Grass clippings are placed in a bin, where they decompose. For $0 \leq t \leq 30$ , the amount of grass clippings remaining in the bin is modeled by $A(t)=6.687(0.931)^{t}$ , where A(t) is measured in pounds and t is measured in days.

Find the average rate of change of A(t) over the interval $0 \leq t \leq 30$ . Indicate units of measure.

$\frac{A(30)-A(0)}{30-0}=-0.197$ (or -0.196 ) lbs/day

[Maximum number: 1]

$\lim _{h \rightarrow 0} \frac{\sqrt{25+h}-5}{h}$

$(\mathrm{A})=0$

(B) $=\frac{1}{10}$

(D) does not exist

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Covered syllabus points

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