Calculus practice
Normal Line at a Point worksheets
Build exact perpendicular normal equations, including vertical normals at stationary points.
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Find the exact normal-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 the negative reciprocal derivative slope to write a normal line.
Worked example
Find the normal to y = x² at x = 1.
The point is (1, 1); the normal slope is -1/2, so y - 1 = -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.
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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.