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KCET2008MathematicsApplication of Derivatives

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

Options

  1. A1
  2. B2 e
  3. C1 e
  4. DNone of the above

Correct answer

C. 1 e

Step-by-step solution

Let y= x x On differentiating w.r.t. x, we get d y d x = x 1 x - x 1 x² = 1- x x² For maxima, put d y d x =0 array lc & 1- x x² =0 & x=1 & x=e array Now, d² y d x² = x² (- 1 x )-(1- x) 2 x (x² )² At x = e , d ² y dx^ 2 0, maxima The maximum value at x = e is y = e e = 1 e

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