Finding the Local Maximum Point for f(x)=xe^(-ax)

[Joza]

Local maximum point...

Homework Statement

f(x)=xe TO THE POWER OF -ax x E R a > o

Show that f(x) has a local maximum and express this point's coordinates in terms of a.

The Attempt at a Solution

I think dy/dx = -axe TO THE POWER OF -ax

Correct?

I don't know where to go after this.

 

[Dick]

Your derivative is wrong. Remember the product rule?

 

[Joza]

Oh product...

Ok so... xe^-ax + e^-ax(1)

Is that right?

 

[Dick]

You used to have a (-a) in front of the first term. Where did that go? I liked it.

 

[Joza]

Ok, I mie be wrong here.

(u)dv/dx + (v)du/dx

So... (x)-ae^-ax + e^-ax( 1) = -axe^-ax + e^-ax

Correct?

 

[Dick]

Finally! Rest of the problem is easy, right?

 

[Joza]

I let it = 0 and solve to get values for x?

 

[Dick]

I think so. Correct me if I'm wrong.

 

[HallsofIvy]

Now, Dick, have you ever been wrong?

 

[Dick]

More times than I can count. I was betting on the Bears last night.