Calculus practice
Slope at a Point worksheets
Find exact curve slopes at rational and standard-unit-circle points across four function families.
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Start with a ready-made worksheet
Find the exact slope of each curve at the given point.
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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
Connect the derivative value with the slope of a curve.
Worked example
Find the slope of y = x² at x = 3.
y' = 2x, so the slope is 6.
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.