connecting a function, its first derivative, and its second derivative

Review connecting a function, its first derivative, and its second derivative for AP Calculus AB and try 2 free AP-style practice questions. 27 questions on this topic in AP Calculus AB · Unit 5 · Analytical Applications of Differentiation.

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Question 1

The figure above shows the graph of $f'$ on $(0, 6)$ , a single smooth arc. At $x = 2$ , the graph of $f$ has

Question 2

Suppose $h'(x) < 0$ and $h''(x) > 0$ for all $x$ in the interval $(2,7)$ . Which of the following must describe the behavior of $h$ on this interval?

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Full practice for AP Calculus AB · Unit 5 · Analytical Applications of Differentiation: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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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

94% sure

Reason: 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

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Connecting a function, its first derivative, and its second derivative: AP Calculus AB Practice Questions | S&D Academy