imo class 12 application of derivatives

Find the maximum value of f(x) = -|x + 1| + 3.

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Find the maximum value of f(x) = -|x + 1| + 3.

  • A. 3
  • B. 4
  • C. 2
  • D. No maximum value

Answer: A) 3

Explanation: Since |x + 1| ≥ 0 for all x, it follows that -|x + 1| ≤ 0. Therefore, f(x) = -|x + 1| + 3 ≤ 3. The maximum value is 3, occurring at x = -1.

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