Manipal MET2014MathematicsApplication of Derivatives

The minimum value of x x is

Options

Ae
B1 e
Ce^2
De^3

Correct answer

A. e

Step-by-step solution

Let aligned f(x) & = x x f^ (x) & = x-1 ( x)^2 aligned Pur f^ (x)=0 , for maxima or minima, we get x-1=0 x=e Now, f^ (x)= ( x)^2 1 x -( x-1) 2 x x ( x)^4 f^ (e)= 1 e -0 1 = 1 e 0 Function is minimum at x=e . Hence, minimum value of f(x) at x=e is f(e)=e .

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