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COMEDK2019MathematicsApplication of Derivatives

The maximum value of x x in (2, ) is

Options

  1. A1
  2. B2 e
  3. Ce
  4. D1 e

Correct answer

D. 1 e

Step-by-step solution

We have, aligned f(x) &= x x f^ (x) &= 1 x x- x 1 x² = 1- x x² aligned For maxima or minima, gathered f^ (x)=0 1- x x² =0 x=1 Now, f^ (x)= - 1 x x²-(1- x) 2 x x⁴ = -x-2 x+2 x x x⁴ gathered

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