Tangent lines using derivatives

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari finds the tangent line to f(x) = x² + 3x − 1 at x = 1. Write it as y = mx + b.

   y = 5x - 2
2. 2.

   Bo finds the tangent line to f(x) = 2x² − x + 4 at x = 2. Write it as y = mx + b.

   y = 7x - 4
3. 3.

   Esme finds the tangent line to f(x) = x² − 4x + 6 at x = 3. Write it as y = mx + b.

   y = 2x - 3
4. 4.

   Jun finds the tangent line to f(x) = 3x² + 2x − 5 at x = -1. Write it as y = mx + b.

   y = -4x - 8
5. 5.

   Kira writes the tangent line to f(x) = 2x³ − 5x at x = 2 as y = mx + b. What is b?

   -32
6. 6.

   Luz writes the tangent line to f(x) = 3x³ + 4x at x = -1 as y = mx + b. What is b?

   6
7. 7.

   Milo writes the tangent line to f(x) = −2x³ + 6x at x = 2 as y = mx + b. What is b?

   32
8. 8.

   Noah writes the tangent line to f(x) = 2x³ + 3x at x = 1 as y = mx + b. What is b?

   -4
9. 9.

   The tangent line to y = f(x) at x = 2 is y = 4x − 3. Pia reads off f(2) and f′(2). Which pair is right?

   • f(2) = 4 and f′(2) = 5
   • f(2) = 5 and f′(2) = 5/2
   • f(2) = -3 and f′(2) = 4
   • f(2) = 5 and f′(2) = 4
10. 10.

    The tangent line to y = f(x) at x = 3 is y = −2x + 7. Ren reads off f(3) and f′(3). Which pair is right?

    • f(3) = 7 and f′(3) = -2
    • f(3) = -2 and f′(3) = 1
    • f(3) = 1 and f′(3) = -2
    • f(3) = 1 and f′(3) = 1/3