Question

for what intervals is f(x)=xe^x concave up and concave down

Answer 1

Hehe. I'm taking calculus AB right now :D Kinda. Not really doing anything in the class since it's almost done

Here's how you'd solve it: You'd find where the second derivative of f(x) is positive, and where it's negative. The second derivative of F(X) =xe^x ends up being:(x+2)e^x

You find the roots of it, the only one ends up being -2. Looking at the graph, we can see that before -2, the second derivative is negative, and afterwards it's positive.

So the graph is concave DOWN for \[(-infty,-2)\]
And the graph is concave UP for
(-2,infinity)