Curve Sketching: The First Derivative Test (Calculus I)
Free printable Calculus I curve-sketching worksheet: find critical points, test the sign of f' on each side, classify local maxima and minima, and state increasing and decreasing intervals. Answers computed by solving f'(x) = 0 and sampling signs.
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Calculus I · Math worksheet
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Math
Curve Sketching: The First Derivative Test
Find f'(x), solve f'(x) = 0, then test the sign of f' on each side of every critical point. f is increasing where f' > 0 and decreasing where f' < 0; a sign change from + to - is a local maximum and from - to + is a local minimum.
- 1.Find all critical points of f(x) = -x³ - 3x² + 24x + 1 and classify each one as a local maximum or a local minimum using the first derivative test.
- 2.Find the intervals on which f(x) = -x³ + 12x² - 36x + 4 is increasing and the intervals on which it is decreasing.
- 3.Find all critical points of f(x) = x³ - 3x² - 24x + 4 and classify each one as a local maximum or a local minimum using the first derivative test.
- 4.Find the intervals on which f(x) = x³ - 6x² - 15x - 3 is increasing and the intervals on which it is decreasing.
- 5.Find all critical points of f(x) = x³ - 3x² - 24x and classify each one as a local maximum or a local minimum using the first derivative test.
- 6.Find the intervals on which f(x) = x³ + 3x² + 1 is increasing and the intervals on which it is decreasing.
- 7.Find all critical points of f(x) = -x³ + 9x² - 3 and classify each one as a local maximum or a local minimum using the first derivative test.
- 8.Find the intervals on which f(x) = x³ - 15x² + 48x + 3 is increasing and the intervals on which it is decreasing.
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