The number of downloads of a mobile app, in thousands, is modeled by a differentiable function , where is the number of days since its release. Which of the following is the best interpretation of ?
interpreting the meaning of the derivative in context
Review interpreting the meaning of the derivative in context for AP Calculus AB and try 2 free AP-style practice questions. 24 questions on this topic in AP Calculus AB · Unit 4 · Contextual Applications of Differentiation.
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The amount of fuel remaining in a rocket, in kilograms, is modeled by the differentiable function for , where is measured in seconds since launch. Which of the following is the best interpretation of the instantaneous rate of change of at ?
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Answer, then see why
The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?
Not quite. The answer is B.
Why the other options are wrong
AI grading for free-response
Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.
Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sureReason: Correctly identifies demand for gasoline as inelastic.
Evidence: "The price of gasoline rises and the quantity falls only a little."
Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."