Match a function with its derivatives

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Bo reads the parabola graph of f′ in the figure. What does it tell about f?

   • f has just one extremum, a local min at x = 3
   • f has a local max at x = 1 and a local min at x = 5
   • f has a local min at x = 1 and a local max at x = 5
   • f is 0 at x = 1 and x = 5
2. 2.

   Esme reads the parabola graph of f′ in the figure. What does it tell about f?

   • f has just one extremum, a local max at x = −1
   • f has a local min at x = 1 and a local max at x = −3
   • f is 0 at x = −3 and x = 1
   • f has a local max at x = 1 and a local min at x = −3
3. 3.

   Jun reads the parabola graph of f′ in the figure. What does it tell about f?

   • f has just one extremum, a local max at x = 3
   • f has a local min at x = 6 and a local max at x = 0
   • f is 0 at x = 0 and x = 6
   • f has a local max at x = 6 and a local min at x = 0
4. 4.

   f′(x) = (x + 5)(x − 1). Luz looks for where f is increasing and f′ is increasing too. Where is that?

   • −5 < x < −2
   • x > 1
   • x > −2
   • x < −5 or x > 1
5. 5.

   f′(x) = x(x − 6). Milo looks for where f is increasing and f′ is increasing too. Where is that?

   • x > 3
   • x < 0 or x > 6
   • 0 < x < 3
   • x > 6
6. 6.

   f′(x) = (x + 1)(x − 3). Noah looks for where f is increasing and f′ is increasing too. Where is that?

   • x > 3
   • x < −1 or x > 3
   • x > 1
   • −1 < x < 1
7. 7.

   f′(x) = x² − 6x + 8. Pia wants the x where f is decreasing fastest. At what x is that?

   3
8. 8.

   f′(x) = x² − 8x + 12. Ren wants the x where f is decreasing fastest. At what x is that?

   4
9. 9.

   f′(x) = x² − 10x + 16. Tala wants the x where f is decreasing fastest. At what x is that?

   5
10. 10.

    f′(x) = x² + 2x − 15. Zee wants the x where f is decreasing fastest. At what x is that?

    -1