AP Calculus BC 4.1 Interpreting the Meaning of the Derivative in Context - Exam Style Questions - MCQs - New Syllabus
Question
A cell phone was plugged into a charger. The battery life of the cell phone, in percent of battery life remaining, can be modeled by a differentiable function \(P(t)\), where \(t\) is the number of minutes after the phone was plugged into the charger and \(0 \le t \le 20\). Which of the following is the best interpretation of \(P'(10) = 1.5\)?
(A) Ten minutes after the phone was plugged into the charger, the battery life was changing at a rate of \(1.5\) percent per minute.
(B) Ten minutes after the phone was plugged into the charger, the rate of change in the battery life was changing by \(1.5\) percent per minute per minute.
(C) During the first ten minutes that the phone was plugged into the charger, the battery life of the phone was changing at an average rate of \(1.5\) percent per minute.
(D) During the first ten minutes that the phone was plugged into the charger, the rate of change in the battery life was changing at an average rate of \(1.5\) percent per minute per minute.
(B) Ten minutes after the phone was plugged into the charger, the rate of change in the battery life was changing by \(1.5\) percent per minute per minute.
(C) During the first ten minutes that the phone was plugged into the charger, the battery life of the phone was changing at an average rate of \(1.5\) percent per minute.
(D) During the first ten minutes that the phone was plugged into the charger, the rate of change in the battery life was changing at an average rate of \(1.5\) percent per minute per minute.
Calc-OkQuestion
A car travels \(100\) km at constant speed \(v\). The amount of fuel used (liters) is modeled by a differentiable function \(F(v)\). Which is a correct interpretation of \(F'(50)>F'(80)\)?
(A) Driving at \(50\) km/hr uses more fuel than driving at \(80\) km/hr.
(B) The rate at which \(50\) liters is used is greater than the rate at which \(80\) liters is used.
(C) The rate of change of the speed is greater at \(50\) km/hr than at \(80\) km/hr.
(D) The rate of change of liters of fuel used with respect to speed is greater at \(50\) km/hr than at \(80\) km/hr.
(B) The rate at which \(50\) liters is used is greater than the rate at which \(80\) liters is used.
(C) The rate of change of the speed is greater at \(50\) km/hr than at \(80\) km/hr.
(D) The rate of change of liters of fuel used with respect to speed is greater at \(50\) km/hr than at \(80\) km/hr.
▶️ Answer/Explanation
Detailed solution
\(F'(v)\) measures how rapidly fuel used changes with respect to speed. \(F'(50)>F'(80)\) ⇒ increasing speed near \(50\) km/hr increases fuel usage faster than increasing speed near \(80\) km/hr.
✅ Answer: (D)