Calculus practice
Tangent Line at a Point worksheets
Build exact point-slope tangent equations, including horizontal tangents, for four function families.
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Find the exact tangent-line equation at the given point on each curve.
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Customize this worksheetDifferentiate, evaluate, then build the line
Every problem gives an exact input. Keep fractions, radicals, pi, powers of e and logarithms exact while finding the point and slope.
Learning objective
What this activity builds
Use a derivative and a point on a curve to write its tangent line.
Worked example
Find the tangent to y = x² at x = 1.
The point is (1, 1) and the slope is 2, so y - 1 = 2(x - 1).
Differentiate first, evaluate both the function and derivative at the specified input, then use the exact point and slope.
Teaching notes
Make the practice count
- Keep fractions, radicals, pi, e and logarithms exact.
- Use the original function to find the point on the curve.
- For a normal line, check whether the tangent is horizontal before taking a negative reciprocal.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose 6, 8, or 10 problems and one or more polynomial, rational, exponential or trigonometric families. Exact answers retain fractions, radicals, pi, e and logarithms.