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KCET2020MathematicsIndefinite Integration

The maximum value of _ e x x , if x>0 is

Options

  1. Ae
  2. B1
  3. C1 e
  4. D- 1 e

Correct answer

C. 1 e

Step-by-step solution

Let y= _ e x x d y d x = x 1 x - _ e x 1 x² = 1- _ e x x² For maximum, put d y d x =0 1- _ e x=0 _ e x=1 x=e Now, d² y d x² = x² (0- 1 x )- (1- _ e x )(2 x) x⁴ = -x-2 x (1- _ e x ) x⁴ ( d² y d x² )_ at x=e < 0 y(e)= _ e e e = 1 e

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