imo class 12 application of derivatives

The absolute maximum value of f(x) = x³ - 3x on [-2, 2] is:

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The absolute maximum value of f(x) = x³ - 3x on [-2, 2] is:

  • A. -2
  • B. 2
  • C. 4
  • D. 18

Answer: B) 2

Explanation: f'(x) = 3x² - 3 = 0 → x = ±1. Evaluate f(x) at boundaries and critical points: f(-2) = -2, f(-1) = 2, f(1) = -2, f(2) = 2. Absolute maximum is 2.

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