Second and higher derivatives

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari differentiates f(x) = 2x⁵ − x⁴ + 3x³ three times. What is f‴(1)?

   114
2. 2.

   Bo differentiates f(x) = −3x⁵ + 2x⁴ + 4x³ three times. What is f‴(2)?

   -600
3. 3.

   Esme differentiates f(x) = 3x⁵ + 5x⁴ − 2x³ three times. What is f‴(-1)?

   48
4. 4.

   Jun differentiates f(x) = 2x⁵ + 3x⁴ − 5x³ three times. What is f‴(1)?

   162
5. 5.

   Kira spots the pattern in the first few derivatives. What is the 10th derivative of 1/x?

   • −10!/x¹¹
   • 10/x¹¹
   • 10!/x¹⁰
   • 10!/x¹¹
6. 6.

   Luz spots the pattern in the first few derivatives. What is the 7th derivative of 1/x?

   • −7!/x⁷
   • −7/x⁸
   • 7!/x⁸
   • −7!/x⁸
7. 7.

   Milo spots the pattern in the first few derivatives. What is the 6th derivative of ln x?

   • 5!/x⁶
   • −5!/x⁵
   • −5!/x⁶
   • −6!/x⁶
8. 8.

   Noah spots the pattern in the first few derivatives. What is the 5th derivative of ln x?

   • 4!/x⁴
   • 5!/x⁵
   • 4!/x⁵
   • −4!/x⁵
9. 9.

   f(x) = kx³ + 3x², and f″(1) = 30. Pia solves for the number k. What is k?

   4
10. 10.

    f(x) = kx³ − 2x², and f″(2) = 44. Ren solves for the number k. What is k?

    4