The derivative as a limit; slope of a tangent

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Bo works out f′(3) for f(x) = 18/x as the limit of [f(3 + h) − f(3)]/h as h → 0. What is f′(3)?

   -2
2. 2.

   Esme works out f′(4) for f(x) = 8/x as the limit of [f(4 + h) − f(4)]/h as h → 0. What is f′(4)?

   -1/2
3. 3.

   Kira expands f(2 + h) for f(x) = 2x³ and takes the limit of [f(2 + h) − f(2)]/h as h → 0. What is f′(2)?

   24
4. 4.

   Luz expands f(-2 + h) for f(x) = 4x³ and takes the limit of [f(-2 + h) − f(-2)]/h as h → 0. What is f′(-2)?

   48
5. 5.

   Milo expands f(2 + h) for f(x) = -3x³ and takes the limit of [f(2 + h) − f(2)]/h as h → 0. What is f′(2)?

   -36
6. 6.

   Noah expands f(4 + h) for f(x) = 2x³ and takes the limit of [f(4 + h) − f(4)]/h as h → 0. What is f′(4)?

   96
7. 7.

   Pia finds the tangent to f(x) = x² + 3 at x = 2, using a limit for the slope. Written as y = mx + b, what is b?

   -1
8. 8.

   Ren finds the tangent to f(x) = x² − 1 at x = 3, using a limit for the slope. Written as y = mx + b, what is b?

   -10
9. 9.

   Tala finds the tangent to f(x) = x² + 5 at x = -2, using a limit for the slope. Written as y = mx + b, what is b?

   1
10. 10.

    Zee finds the tangent to f(x) = x² + 4 at x = 1, using a limit for the slope. Written as y = mx + b, what is b?

    3