MHT CET202013 Oct 2020Evening ShiftMathematicsApplication of DerivativesActual

The maximum value of the function x x , x 0 is

Options

Ae²
B1 e
C1 e²
De

Correct answer

B. 1 e

Step-by-step solution

Let y= x x dy dx = x 1 x - x x ² = 1- x x ² Put d y d x =0 , we get aligned 1- x=0 & x=1 x= e x=e Now d² y d x² &= x² (- 1 x )-(1- x)(2 x) x⁴ = -x-2 x+2 x x x⁴ &= 2 x-3 x³ aligned At x=e, d² y d x² < 0 from (1), maximum value is y= 1 e

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