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AP EAMCET · Maths · Application of Derivatives

If m and M are the absolute minimum and absolute maximum values of the function \(\mathrm{f}(\mathrm{x})=2 \sqrt{2} \sin \mathrm{x}-\tan \mathrm{x}\) in the interval \([0, \pi / 3]\), then \(\mathrm{m}+\mathrm{M}=\)

  1. A \(-1\)
  2. B \(0\)
  3. C \(1\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1\)

Step-by-step Solution

Detailed explanation

\(f'(x) = 2\sqrt{2}\cos x - \sec^2 x\) \(f'(x) = 0 \implies 2\sqrt{2}\cos x - \frac{1}{\cos^2 x} = 0 \implies 2\sqrt{2}\cos^3 x = 1 \implies \cos x = \frac{1}{\sqrt{2}}\) \(x = \pi/4\) \(f(0) = 2\sqrt{2}\sin(0) - \tan(0) = 0 - 0 = 0\)…