AP Calculus AB 4.1 Interpreting the Meaning of the Derivative in Context - MCQs - Exam Style Questions
No-Calc Question
A cell phone is charging. The battery life (percent remaining) is modeled by a differentiable function \(P(t)\), where \(t\) is minutes after plugging in and \(0\le t\le 20\). Which statement best interprets \(P'(10)=1.5\)?
(A) Ten minutes after plugging in, the battery life was changing at \(1.5\) percent per minute.
(B) Ten minutes after plugging in, the rate of change of the battery life was changing by \(1.5\) percent per minute per minute.
(C) During the first ten minutes, the battery life changed at an average rate of \(1.5\) percent per minute.
(D) During the first ten minutes, the rate of change changed at an average rate of \(1.5\) percent per minute per minute.
(B) Ten minutes after plugging in, the rate of change of the battery life was changing by \(1.5\) percent per minute per minute.
(C) During the first ten minutes, the battery life changed at an average rate of \(1.5\) percent per minute.
(D) During the first ten minutes, the rate of change changed at an average rate of \(1.5\) percent per minute per minute.
▶️ Answer/Explanation
\(P'(10)\) is the instantaneous rate of change of the battery percentage at \(t=10\) minutes, with units “percent per minute.”
✅ Answer: (A)
✅ Answer: (A)
Calc-Ok Question
The function \(f\) models the amount of time \(f(v)\) (in hours) to ride a bicycle from \(A\) to \(B\), where \(v\) is the average speed in miles per hour (mph). What are the units of \(f'(v)\)?
(A) mph
(B) hours
(C) mph per hour
(D) hours per mph
(B) hours
(C) mph per hour
(D) hours per mph
▶️ Answer/Explanation
\(f'(v)=\dfrac{df}{dv}\) has numerator “hours” and denominator “mph.”
✅ Answer: (D) hours per mph
✅ Answer: (D) hours per mph