Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = 3

Let f(x) = −3x3 − 9x2 + 7x + 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −3x3 − 9x2 + 7x + 8x = 3
f′(3) =
2.Easy
xyx = −1

Let f(x) = 2x4 − x2 − 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x4 − x2 − 3x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = (2x − 3)3. Find f′(2).

f(x) = (2x − 3)3x = 2
f′(2) =
4.Medium
xyx = −1

Let f(x) = (−2x − 3)4. Find f′(−1).

f(x) = (−2x − 3)4x = −1
f′(−1) =
5.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x + 5
x =
6.Hard
xyx = 3

The tangent line to f(x) = 2x2 − 3x + 4 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 3x + 4x = 3
b =

Answer key

  1. 1. f′(3) = −128
  2. 2. f′(−1) = −6
  3. 3. f′(2) = 6
  4. 4. f′(−1) = 8
  5. 5. x = 3
  6. 6. b = −14

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