1. ## Graph

Using calculus and technology, sketch the graph of f(x)=xe^x
.Be sure to note any relative and/or absolute extrema, point(s) of inflection and any asymptotic features. Show all symbolic work that helps you arrive at your conclusions.

2. Originally Posted by venikUSA
Using calculus and technology, sketch the graph of f(x)=xe^x
.Be sure to note any relative and/or absolute extrema, point(s) of inflection and any asymptotic features. Show all symbolic work that helps you arrive at your conclusions.

What is your question? Graph it on your calculator. To find extrema, take the derivative and do a sign chart analysis. For inflection points, use the 2nd derivative.

3. what are the first and second derivatives of f(x)=xe^x?

4. Originally Posted by venikUSA
what are the first and second derivatives of f(x)=xe^x?
use the product rule to find them ...

5. Originally Posted by venikUSA
what are the first and second derivatives of f(x)=xe^x?
Use the product rule:

Let $f = x$ and $g = e^x$

$(f ')(g) + (f) (g ')$

*****

$f(x) = xe^x$

$f '(x) = (1)(e^x) + (x)(e^x)$

$f "(x) = e^x + \left[(1)(e^x) + (x)(e^x)\right]$

Then simplify. If you are not comfortable using the product rule, you need to practice. It will be something you frequently use in calculus.