AP EAMCET2009MathematicsApplication of Derivatives

The maximum value of x x , 0 < x < is

Options

Ae
B1
Ce⁻¹

Correct answer

Step-by-step solution

Let y= x x d y d x = x 1 x - x x^2 = 1- x x^2 Put d y d x =0 x=1 x=e Now, d^2 y d x^2 = x^2 (- 1 x )-(1- x) 2 x (x^2 )^2 =- (3-2 x) x^3 ( d^2 y d x^2 )_ (x=e) = -(3-2) e^3 =- 1 e^3 < 0 , maxima Hence, maximum value at x=e is 1 e .

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