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KCET2018MathematicsApplication of Derivatives

( f(x)=x^ x ) has stationary point at

Options

  1. A( x= )
  2. B( x= 1 e )
  3. C( x=1 )
  4. D( x = e )

Correct answer

B. ( x= 1 e )

Step-by-step solution

Given that, f(x)=x^ x f(x)=x x 1 f(x) f^ (x)= x+1 f^ (x)=f(x)( x+1)=x^ x ( x+1) Stationary point is given by f^ (x)=0x^ x ( x+1)=0 x=-1 x=e⁻¹ x= 1 e

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