Worksheets · Calculus

Slope at a point worksheet

The derivative is a formula for the slope everywhere. To get the slope at one point, find the derivative first and only then put the x value in.

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Sigma Prep · sigmaprep.io/worksheets

Name

The Slope at a Point

Date Period

Find the slope at the given point.

  1. f(x)=−10x−9x3. Find f′(64)
  2. Use the definition to find f′(3) for f(x)=−x2−x+1: lim⁡h→0f(3+h)−f(3)h
  3. f(x)=6x3+6x. Find f′(2)
  4. Use the definition to find f′(−1) for f(x)=x2−6x+4: lim⁡h→0f(−1+h)−f(−1)h
  5. f(x)=x3−18x3. Find f′(8)
  6. Use the definition to find f′(3) for f(x)=3x2−5x−3: lim⁡h→0f(3+h)−f(3)h
  7. f(x)=−6x+4x. Find f′(16)
  8. Use the definition to find f′(3) for f(x)=−3x2−2x+5: lim⁡h→0f(3+h)−f(3)h
  9. f(x)=3x3+1x. Find f′(3)
  10. Use the definition to find f′(−3) for f(x)=2x2+2x−4: lim⁡h→0f(−3+h)−f(−3)h
  11. f(x)=12x+2x. Find f′(4)
  12. Use the definition to find f′(1) for f(x)=x2−x+1: lim⁡h→0f(1+h)−f(1)h
  13. f(x)=−8x−4x. Find f′(16)
  14. Use the definition to find f′(2) for f(x)=−x2−6x−1: lim⁡h→0f(2+h)−f(2)h
  15. f(x)=6x+12x3. Find f′(64)
  16. Use the definition to find f′(0) for f(x)=2x2+3x−5: lim⁡h→0f(0+h)−f(0)h
  17. f(x)=8x−18x3. Find f′(64)
  18. Use the definition to find f′(2) for f(x)=−2x2−2x+5: lim⁡h→0f(2+h)−f(2)h
  19. f(x)=12x−4x2. Find f′(4)
  20. Use the definition to find f′(0) for f(x)=3x2+x+1: lim⁡h→0f(0+h)−f(0)h

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Slope at a PointAnswer keyVersion 1

Date Period

Find the slope at the given point.

  1. f(x)=−10x−9x3. Find f′(64)−1316
  2. Use the definition to find f′(3) for f(x)=−x2−x+1: lim⁡h→0f(3+h)−f(3)h−7
  3. f(x)=6x3+6x. Find f′(2)1412
  4. Use the definition to find f′(−1) for f(x)=x2−6x+4: lim⁡h→0f(−1+h)−f(−1)h−8
  5. f(x)=x3−18x3. Find f′(8)3812
  6. Use the definition to find f′(3) for f(x)=3x2−5x−3: lim⁡h→0f(3+h)−f(3)h13
  7. f(x)=−6x+4x. Find f′(16)−2532
  8. Use the definition to find f′(3) for f(x)=−3x2−2x+5: lim⁡h→0f(3+h)−f(3)h−20
  9. f(x)=3x3+1x. Find f′(3)7289
  10. Use the definition to find f′(−3) for f(x)=2x2+2x−4: lim⁡h→0f(−3+h)−f(−3)h−10
  11. f(x)=12x+2x. Find f′(4)238
  12. Use the definition to find f′(1) for f(x)=x2−x+1: lim⁡h→0f(1+h)−f(1)h1
  13. f(x)=−8x−4x. Find f′(16)−6364
  14. Use the definition to find f′(2) for f(x)=−x2−6x−1: lim⁡h→0f(2+h)−f(2)h−10
  15. f(x)=6x+12x3. Find f′(64)58
  16. Use the definition to find f′(0) for f(x)=2x2+3x−5: lim⁡h→0f(0+h)−f(0)h3
  17. f(x)=8x−18x3. Find f′(64)18
  18. Use the definition to find f′(2) for f(x)=−2x2−2x+5: lim⁡h→0f(2+h)−f(2)h−10
  19. f(x)=12x−4x2. Find f′(4)258
  20. Use the definition to find f′(0) for f(x)=3x2+x+1: lim⁡h→0f(0+h)−f(0)h1

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

f(x)=x3−4x. Find f′(2)

  1. The derivative is 3x squared minus 4.
  2. Put 2 in for x: 3 times 4 is 12.
  3. 12 minus 4 is 8.

The answer is 8.

Where students go wrong

Putting the point into f instead of f'. That gives the height of the curve there, not its slope.

Also called derivative at a point, instantaneous rate of change, evaluate f'(a) or slope of the curve.

What you can put on this worksheet

The slope at a point
f(x)=−6x+4x2. Find f′(4) → −138
At a point
Use the definition to find f′(0) for f(x)=2x2+3x−5: lim⁡h→0f(0+h)−f(0)h → 3
The slope at a point
Find dydx at (2,1) on x2+y2=5 → −2

Questions about these worksheets

Yes. Every slope at a point sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the slope at a point questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: the slope at a point, at a point and the slope at a point. Tick as many as you want and set how many of each, or let it spread them evenly.

Putting the point into f instead of f'. That gives the height of the curve there, not its slope.