imo class 12 application of derivatives

Find the maximum value of f(x) = sin x + cos x in (0, π).

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Find the maximum value of f(x) = sin x + cos x in (0, π).

  • A. 1
  • B. 2
  • C. 1/√2
  • D. √2

Answer: D) √2

Explanation: f(x) = √2( (1/√2)sin x + (1/√2)cos x ) = √2 sin(x + π/4). The maximum value of sine function is 1, so the maximum value is √2(1) = √2 at x = π/4.

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