Tangent lines using derivatives

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Bo writes the tangent line to f(x) = 20/x at x = 4 as y = mx + b. What is b?

   10
2. 2.

   Esme writes the tangent line to f(x) = −6/x at x = 3 as y = mx + b. What is b?

   -4
3. 3.

   Jun writes the tangent line to f(x) = 15/x at x = 5 as y = mx + b. What is b?

   6
4. 4.

   Kira looks for every x where f(x) = x³ − 3x² − 9x + 5 has a horizontal tangent. List them, separated by commas.

   -1, 3
5. 5.

   Luz looks for every x where f(x) = x³ + 3x² − 24x + 1 has a horizontal tangent. List them, separated by commas.

   -4, 2
6. 6.

   Milo looks for every x where f(x) = x³ − 9x² + 15x has a horizontal tangent. List them, separated by commas.

   1, 5
7. 7.

   Noah looks for every x where f(x) = x³ − 3x² − 24x + 7 has a horizontal tangent. List them, separated by commas.

   -2, 4
8. 8.

   Ren finds the tangent line to f(x) = x(x − 2)³ at x = 3. Which is it?

   • y = 10x + 3
   • y = 10x + 33
   • y = 10x − 27
   • y = 3x − 6
9. 9.

   Tala finds the tangent line to f(x) = 4/(x² + 1) at x = 1. Which is it?

   • y = 2x
   • y = −2x
   • y = −2x + 2
   • y = −2x + 4
10. 10.

    Zee finds the tangent line to f(x) = √(2x + 5) at x = 2. Which is it?

    • y = 3x − 3
    • y = (1/3)x + 3
    • y = (1/3)x + 11/3
    • y = (1/3)x + 7/3