AP Calculus AB 2.3: Estimating Derivatives

A student starts reading a book at time t=0 minutes and continues reading for the next 10 minutes. The rate

at which the student reads is modeled by the differentiable function R, where R(t) is measured in words per

minute. Selected values of R(t) are given in the table shown.

Model Solution

Scoring

A Approximate $R^{\prime}(1)$ using the average rate of change of R over the interval $0 \leq t \leq 2$. Show the work

that leads to your answer. Indicate units of measure.

$$\begin{aligned} & R^{\prime}(1) \approx \frac{R(2)-R(0)}{2-0} \\ & =\frac{100-90}{2}=\frac{10}{2}=5 \text { words per minute per minute } \end{aligned}$$

Scoring Notes for Part A

- To earn P1, a response must present the answer along with the supporting work of a difference and a

quotient using values from the table.

○ $\frac{100-90}{2-0}, \frac{10}{2-0}, \frac{100-90}{2}$, or $\frac{R(2)-R(0)}{2-0}=5$ is sufficient to earn P1.

○ $\frac{R(2)-R(0)}{2-0}$ by itself is not sufficient to earn P1.

- P2 is earned for correct units, whether or not they are attached to a numerical value for the average

rate of change.

- P2 is also earned for the units "words/minute ${ }^{2}$."