Calculus
Graphing Derivatives worksheets
Sketch derivative graphs from aligned polynomial, rational, and trigonometric function graphs, with an optional explicit equation.
Preview and downloadCalculus practice
Horizontal Tangents on Graphs worksheets
Plot or inspect polynomial, rational, and trigonometric functions and identify every horizontal tangent coordinate in the displayed interval.
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Graph when requested, then mark every point where the tangent is horizontal in the displayed interval.
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Customize this worksheetRead the whole displayed interval
Aligned axes, explicit windows, and separate rational branches make slope and shape claims visible rather than implied.
Learning objective
What this activity builds
Relate zeros of f' to visible stationary coordinates while preserving the original function domain.
Worked example
Find horizontal tangents of f(x)=x^3-3x on the displayed window.
(-1,2) and (1,-2).
f'(x)=3x^2-3 vanishes at x=-1 and x=1; substituting gives both coordinates.
Teaching notes
Make the practice count
- A horizontal tangent needs a coordinate, not only an x-value.
- Check all stationary inputs inside the shown interval.
- Do not count a pole as a tangent point.
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Choose your options, update the preview, then download the exact same pages.
Choose a nonempty set of function families. Every graph uses a stated window and keeps discontinuous branches separate.
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