Here's the question:

Function (X+2) e^ -3X. Find intervals where it is increasing and decreasing. Find the extreme values and indicate the max or min.

Here is my best attempt at this problem:

Y= (X+2) e^ -3X

Y' = (e^-3X) + (X+2) ((e^-3x)(-3)

Y' = (e^-3X) (1+ (-3(X+2))

Y' = (e^-3X) (1- 3X-6))

Y' = -(e^-3X) (3X+5)

Now I am stuck. I don't know what to do.

The only thing I can think of is trying to find a value forXthat would causeY' = 0, but I haven't been able to do that.

Can anyone help me?