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KCET2018MathematicsApplication of Derivatives

The maximum value of ( ( 1 x )^ x ) is

Options

  1. A( e )
  2. B( e^ e )
  3. C( e^ 1 / e )
  4. D( ( 1 e )^ 1 / e )

Correct answer

C. ( e^ 1 / e )

Step-by-step solution

Let us suppose f=x^ -x f=-x x 1 f d f d x =-(1+ x) So, d f d x =-f (1+ _ e x ) For maximum; 1+ _ e x=0 x=e⁻¹ x= 1 e Therefore, maximum value of given function is ( 1 1 / e )=e^ 1 e

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