Question

The interval in which the function f is given by f(x) = x² e^-x is strictly increasing, is: ____________.

पर्याय

• `(- infty, 0)`

• (0, 2)

• `(- infty, infty)`

• `(2, infty)`

Answer 1

The interval in which the function f is given by f(x) = x² e^-x is strictly increasing, is: (0, 2).

Explanation:

Here,it is given that the function `"f'" ("x") = "d"/"dx" ("x"^2 "e"^"-x")`

`= "x"^2 "e"^"-x" (-1) + 2 "xe"^"-x"`

`=> "f'" ("x") = "e"^"-x" (2"x" - "x"^2) > 0`

if `(2"x" - "x"^2) > 0`

i.e. if x(x – 2 ) < 0 i.e. if 0 < x < 2. Hence f is strictly increasing on (0,2)