Match a function with its derivatives

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari studies the graph of f described in the figure. Where is f′(x) negative?

   • at x = 1 and x = 4, where f turns
   • x < 1 or x > 4
   • 1 < x < 4
   • x > 1
2. 2.

   Esme studies the graph of f described in the figure. Where is f′(x) negative?

   • x > 0
   • x < 0 or x > 5
   • 0 < x < 5
   • at x = 0 and x = 5, where f turns
3. 3.

   Jun studies the graph of f described in the figure. Where is f′(x) negative?

   • x < −3 or x > 2
   • x > 2
   • −3 < x < 2
   • at x = −3 and x = 2, where f turns
4. 4.

   Kira reads the graph of f′ in the figure. At what x does f have a local maximum?

   5/2
5. 5.

   Luz reads the graph of f′ in the figure. At what x does f have a local maximum?

   4
6. 6.

   Milo reads the graph of f′ in the figure. At what x does f have a local maximum?

   3/2
7. 7.

   Noah reads the graph of f′ in the figure. At what x does f have a local maximum?

   11/3
8. 8.

   f(x) = x² − 4x. Pia sketches the graph of f′. Which describes it?

   • a falling line crossing the x-axis at x = 2
   • a rising line crossing the x-axis at x = 2
   • a rising line crossing the x-axis at x = 4
   • a parabola crossing the x-axis at x = 0 and x = 4
9. 9.

   f(x) = 9x − x². Tala sketches the graph of f′. Which describes it?

   • a falling line crossing the x-axis at x = 9/2
   • a falling line crossing the x-axis at x = 9
   • a parabola crossing the x-axis at x = 0 and x = 9
   • a rising line crossing the x-axis at x = 9/2
10. 10.

    f(x) = x² − 10x. Zee sketches the graph of f′. Which describes it?

    • a parabola crossing the x-axis at x = 0 and x = 10
    • a rising line crossing the x-axis at x = 5
    • a falling line crossing the x-axis at x = 5
    • a rising line crossing the x-axis at x = 10