determining intervals on which a function is increasing or decreasing

Review determining intervals on which a function is increasing or decreasing for AP Calculus AB and try 2 free AP-style practice questions. 15 questions on this topic in AP Calculus AB · Unit 5 · Analytical Applications of Differentiation.

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Question 1

The graph of $f'$ is shown above for $-3\le x\le3$ . On which interval is $f$ decreasing?

Question 2

Suppose $f$ is differentiable for all real $x$ , with $f'(x) < 0$ for $x < 2$ , $f'(2) = 0$ , and $f'(x) > 0$ for $x > 2$ . If $g(x) = f(x - 5)$ , on what interval is $g$ increasing?

13 more questions on this topic

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."

Determining intervals on which a function is increasing or decreasing: AP Calculus AB Practice Questions | S&D Academy