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The set of all points for which f(x)=x^(...

The set of all points for which `f(x)=x^(2)e^(-x)` stricltly increasing is

A

`(0,2)`

B

`(2,oo)`

C

`(-2,0)`

D

`(-oo,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `f(x)=x^(2)e^(-x)`
`impliesf'(x)=2xe^(-x)-x^(2)e^(-x)=xe^(-x)(2-x)`
Sincd `f(x)` is strictly increasing.
`:.f'(x)gt0impliesxe^(-x)(2-x)gt0`
`impliesx(2-x)gt0impliesxgt0,2-xgt0`
`implies xgt0,2gtximplies0ltxlt2`
`impliesx epsilon(0,2)`
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