The function f defined by `f(x)`=`(x+2)``e^(−x)`is

Options

A. decreasing in for all x
B. increasing in `(-oo,-1)` and decreasing in `(-1,oo)`
C. increasing for all x
D. decreasing in `(-1,oo)` and increasing in `(-oo,0)`

Answer

B

Explanation

We have,
`f(x)=(x+2)e^(-x)rArr f'(x)=e^(-x)-(x+2)e^(-x)=-(x+1)e^(-x)`
`therefore f' (x) ltj 0 `
`rArr -(x+1)e^(-x) lt 0 rArr -(x+1) lt 0 rArr x+1 gt 0 rArr x gt -1`
Hence f(x) is decreasing in `(-1 ,oo)` and increasing in `(-oo,-1)`