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Manipal MET2018MathematicsApplication of Derivatives

The minimum value of x x is equal to

Options

  1. Ae
  2. B1/e
  3. C-1/e
  4. D2/e

Correct answer

C. -1/e

Step-by-step solution

Let (y=x _e x ) On differentiating w.r.t. (x ), we get ( d y d x =x 1 x + x=(1+ x) ) Again, differentiating, we get ( d^2 y d x^2 = 1 x ) Put, ( d y d x =0 ) for maxima or minima. ( aligned & 1+ x=0 & x= 1 e & ( d^2 y d x^2 )_ (x= 1 c ) =e aligned ) ( y ) is minimum at (x= 1 e ) ( y_ = 1 e _e ( 1 e )=- 1 e )

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