The function f(x)=`(x^(2))/(e^(x))` monotonically increasing if

Options

A. `x lt 0` only
B. `x gt 2` only
C. `0 lt x lt 2`
D. `x in (-oo,0)cup (2,oo)`

Answer

C

Explanation

`f(x)=(x^(2))/(e^(x))`
`f'(x)=(2x.e^(x)-e^(x).x^(2))/(e^(x))^(2)`
`f'(x)=(2x-x^(2))/(e^(x))`
as `e^(x)` is a always positive and for monotonically increasing `2x-x^(2)gt0` ltbnrgt ` rarr x^(2)-2xlt0 rarr x(x-2)lt0 rarr x =(0,2)`