Question

Analyze a graph In Exercise,analyze and sketch the graph of the function.Label any relative extrema, points of inflation,and asymptotes.

f(x) = xe - x

Answer 1

Explanation:

Given is a function of x

`f(x) = xe^(-x)`

When y=0 we get x=0 and infinity

Hence x intercept is 0 and one asymptote is x axis.

When x=0 , y =0

`f'(x) = e^(-x)(-x+1)`

`f''(x) = e^(-x)(x-1-1)`

Maxima at x=1, and point of inflection is at x=2

Increasing upto x=1 and then decreases

Graph is enclosed