AP Calculus BC 2.3 Estimating Derivatives of a Function at a Point- MCQs - Exam Style Questions
Question
An airplane’s height above sea level is modeled by a differentiable function \(y=h(t)\), where \(t\) is minutes after takeoff and \(h(t)\) is in feet. The graph of \(h\) is shown for \(0\le t\le15\). Which of the following is the best estimate of the rate at which the plane is rising at \(t=9\) minutes?
(A) \(\tfrac{37{,}275-150}{15-0}\)
(B) \(\tfrac{37{,}275-9{,}775}{15-5}\)
(C) \(\tfrac{37{,}275-16{,}859}{15-7}\)
(D) \(\tfrac{30{,}763-16{,}859}{11-7}\)
(B) \(\tfrac{37{,}275-9{,}775}{15-5}\)
(C) \(\tfrac{37{,}275-16{,}859}{15-7}\)
(D) \(\tfrac{30{,}763-16{,}859}{11-7}\)
▶️ Answer/Explanation
Correct answer: (D)
Use a centered average rate of change around \(t=9\):
\(\displaystyle \frac{h(11)-h(7)}{11-7}=\frac{30{,}763-16{,}859}{4}=3{,}476.\)
This best approximates \(h'(9)\).