Manipal MET2015MathematicsApplication of Derivatives

The greatest value of the function f(x)=x e^ -x in [0, ) , is

Options

A0
B1 e
C-e

Correct answer

B. 1 e

Step-by-step solution

We have, f(x)=x e^ -x On differentiating both sides w.r.t. x , we get f^ (x)=e^ -x (1-x) Put f^ (x)=0 x=1 Now, f(0)=0 and _ x f(x)= _ x x e^ -x = _ x x e^x = _ x 1 ^x =0 Hence, the greatest value of f(x) is 1 e .

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