Second and higher derivatives

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari differentiates f(x) = 2x⁴ − 5x³ + 3x² twice. What is f″(2)?

   42
2. 2.

   Bo differentiates f(x) = 3x⁴ + 2x³ − 5x² twice. What is f″(2)?

   158
3. 3.

   Jun differentiates f(x) = 5x⁴ − 3x³ − 2x² twice. What is f″(-1)?

   74
4. 4.

   Kira follows the pattern of derivatives of 3 sin x. What is the 4th derivative?

   • −3 sin x
   • 3 sin x
   • −3 cos x
   • 3 cos x
5. 5.

   Luz follows the pattern of derivatives of 2 cos x. What is the 3rd derivative?

   • −2 sin x
   • −2 cos x
   • 2 cos x
   • 2 sin x
6. 6.

   Milo follows the pattern of derivatives of e^(2x). What is the 5th derivative?

   • 32e^(2x)
   • 2e^(2x)
   • 64e^(2x)
   • 16e^(2x)
7. 7.

   Noah follows the pattern of derivatives of e^(3x). What is the 4th derivative?

   • 243e^(3x)
   • 81e^(3x)
   • 3e^(3x)
   • 27e^(3x)
8. 8.

   Pia writes f(x) = 27/x as 27x⁻¹ and differentiates twice. What is f″(3)?

   2
9. 9.

   Ren writes f(x) = 5/x as 5x⁻¹ and differentiates twice. What is f″(-1)?

   -10
10. 10.

    Zee writes f(x) = 10/x as 10x⁻¹ and differentiates twice. What is f″(5)?

    4/25