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

Answer:

Step-by-step 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