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KCET2010MathematicsApplication of Derivatives

The set of real values of x for which f(x)= x x is increasing, is

Options

  1. Ax: x e
  2. Bempty
  3. Cx : x < e
  4. D1

Correct answer

A. x: x e

Step-by-step solution

aligned f(x)=& x x f^ (x) &= x 1-x 1 x ( x)² = ( x-1) ( x)² aligned We know that, f ( x ) is increasing (strictly) When f ^ ( x )>0 ( x-1) ( x)² >0 ( x-1)>0 x>1 _ e x > _ e e x > e Hence, x : x e

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