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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. 1.
    Find the absolute maximum and absolute minimum values of f(x) = x³ + 6x² + 9x + 4 on the closed interval [-5, 0].
  2. 2.
    Find the absolute maximum and absolute minimum values of f(x) = x³ + 3x² - 24x - 4 on the closed interval [-6, 3].
  3. 3.
    Find the absolute maximum and absolute minimum values of f(x) = x³ - 15x² + 48x - 5 on the closed interval [0, 10].
  4. 4.
    Find the absolute maximum and absolute minimum values of f(x) = x³ - 9x² + 15x + 1 on the closed interval [-1, 7].
  5. 5.
    Find the absolute maximum and absolute minimum values of f(x) = x³ - 3x + 5 on the closed interval [-3, 3].
  6. 6.
    Find the absolute maximum and absolute minimum values of f(x) = x³ + 6x² + 5 on the closed interval [-5, 2].
  7. 7.
    Find the absolute maximum and absolute minimum values of f(x) = x³ - 3x² - 9x - 2 on the closed interval [-3, 5].
  8. 8.
    Find the absolute maximum and absolute minimum values of f(x) = x³ - 12x on the closed interval [-3, 3].
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