The derivative as a limit; slope of a tangent

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari finds f′(2) for f(x) = 2x² + 3x as the limit of [f(2 + h) − f(2)]/h as h → 0. What is f′(2)?

   11
2. 2.

   Bo finds f′(3) for f(x) = 3x² − 2x as the limit of [f(3 + h) − f(3)]/h as h → 0. What is f′(3)?

   16
3. 3.

   Esme finds f′(4) for f(x) = −2x² + 7x as the limit of [f(4 + h) − f(4)]/h as h → 0. What is f′(4)?

   -9
4. 4.

   Jun finds f′(2) for f(x) = 4x² − 3x as the limit of [f(2 + h) − f(2)]/h as h → 0. What is f′(2)?

   13
5. 5.

   Luz estimates f′(3) from the tangent line drawn in the figure. What is the slope of the tangent at x = 3?

   -2

6. Read this first

   Use this

   A curve y = f(x) with its tangent line at x = -1 drawn on a grid. The tangent passes through (-1, 2) and (3, 8).

7. 6.

   Milo estimates f′(-1) from the tangent line drawn in the figure. What is the slope of the tangent at x = -1?

   3/2
8. 7.

   Noah estimates f′(0) from the tangent line drawn in the figure. What is the slope of the tangent at x = 0?

   5/2
9. 8.

   A limit gives f′(3) = 4, and f(3) = 5. Pia writes the tangent line at x = 3 as y = mx + b. What is b?

   -7
10. 9.

    A limit gives f′(2) = 5, and f(2) = -1. Ren writes the tangent line at x = 2 as y = mx + b. What is b?

    -11
11. 10.

    A limit gives f′(4) = -3, and f(4) = 10. Zee writes the tangent line at x = 4 as y = mx + b. What is b?

    22