Match a function with its derivatives

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari reads the graph of f′ described in the figure. Which must be true about f?

   • f has a local max at x = −1 and a local min at x = 3
   • f has a local min at x = −1 and a local max at x = 3
   • f is negative for −1 < x < 3
   • f is 0 at x = −1 and x = 3
2. 2.

   Bo reads the graph of f′ described in the figure. Which must be true about f?

   • f is 0 at x = −2 and x = 4
   • f has a local max at x = 4 and a local min at x = −2
   • f has a local min at x = 4 and a local max at x = −2
   • f is positive for −2 < x < 4
3. 3.

   Esme reads the graph of f′ described in the figure. Which must be true about f?

   • f has a local min at x = 1 and a local max at x = 5
   • f has a local max at x = 1 and a local min at x = 5
   • f is negative for 1 < x < 5
   • f is 0 at x = 1 and x = 5
4. 4.

   Jun reads the graph of f′ described in the figure. Which must be true about f?

   • f has a local min at x = 0 and a local max at x = −4
   • f is positive for −4 < x < 0
   • f is 0 at x = −4 and x = 0
   • f has a local max at x = 0 and a local min at x = −4
5. 5.

   Kira reads the graph of f′ in the figure. What is f″(x)?

   3
6. 6.

   Luz reads the graph of f′ in the figure. What is f″(x)?

   -3
7. 7.

   Noah reads the graph of f′ in the figure. What is f″(x)?

   2
8. 8.

   f(x) = x³ − 6x². Pia sketches the graph of f″. Which describes it?

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

   f(x) = x³ + 9x². Ren sketches the graph of f″. Which describes it?

   • a rising line crossing the x-axis at x = −3
   • a rising line crossing the x-axis at x = −6
   • a parabola crossing the x-axis at x = 0 and x = −6
   • a falling line crossing the x-axis at x = −3
10. 10.

    f(x) = 3x² − x³. Tala sketches the graph of f″. Which describes it?

    • a parabola crossing the x-axis at x = 0 and x = 2
    • a falling line crossing the x-axis at x = 2
    • a falling line crossing the x-axis at x = 1
    • a rising line crossing the x-axis at x = 1