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Let f(x) be real valued continuous funct...

Let `f(x)` be real valued continuous function on `R` defined as `f(x)=x^(2)e^(-|x|)` then
`f(x)` is increasing in

A

`(0,2)`

B

`(2,oo)`

C

`(-2,0)`

D

`(-oo,2)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
We have
`f(x)=x^(2)e^(-|x|)={(x^(2)e^(-x),xge0),(x^(2)e^(x),xlt0):}`
`f^(')(x)={(xe^(-x)(2-x),xge0),(xe^(x)(x+2),xlt0):}`
`f(x)` is increasing in `(-oo,-2)uu(0,2)`
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