Absolute Extrema on a Closed Interval (Calculus I)
Free printable Calculus I worksheet on the Closed Interval Method: solve f'(x) = 0 for critical points, evaluate f at critical points and endpoints, and identify the absolute maximum and minimum. Every answer computed by a genuine solver.
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Calculus I · Math worksheet
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Absolute Extrema on a Closed Interval
Use the Closed Interval Method: find f'(x), solve f'(x) = 0 for the critical points inside the interval, then evaluate f at each critical point and at both endpoints. The largest value is the absolute maximum and the smallest is the absolute minimum.
- 1.Find the absolute maximum and absolute minimum values of f(x) = x³ + 6x² + 9x + 4 on the closed interval [-5, 0].
- 2.Find the absolute maximum and absolute minimum values of f(x) = x³ + 3x² - 24x - 4 on the closed interval [-6, 3].
- 3.Find the absolute maximum and absolute minimum values of f(x) = x³ - 15x² + 48x - 5 on the closed interval [0, 10].
- 4.Find the absolute maximum and absolute minimum values of f(x) = x³ - 9x² + 15x + 1 on the closed interval [-1, 7].
- 5.Find the absolute maximum and absolute minimum values of f(x) = x³ - 3x + 5 on the closed interval [-3, 3].
- 6.Find the absolute maximum and absolute minimum values of f(x) = x³ + 6x² + 5 on the closed interval [-5, 2].
- 7.Find the absolute maximum and absolute minimum values of f(x) = x³ - 3x² - 9x - 2 on the closed interval [-3, 5].
- 8.Find the absolute maximum and absolute minimum values of f(x) = x³ - 12x on the closed interval [-3, 3].
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