For the function `f(x)=xe^x,` the point

Options

A. `x=0` is a maximum
B. `x=0` is a minimum
C. `x=-1`is a maximum
D. `x=-1`is a minimum

Answer

D

Explanation

Given ,`f(x)=xe^(x)`
`rArr f'(x)=e^(x)+xe^(x)`
for max or min `f'(x)=0`
`rArr e^(x)(1+x)=0rArr x=-1`
`rArr f' '(x)=e^(x)+xe^(x)+e^x[because(d)/(dx)e^(x)=e^(x)]`
`=2e^(x)+xe^(x)`
`f' '(-1)=e^(-1)gt 0`
`therefore` Minima at `x=-1`