Local maximum point

  • Thread starter Joza
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  • #1
Joza
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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.
 

Answers and Replies

  • #2
Dick
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Your derivative is wrong. Remember the product rule?
 
  • #3
Joza
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Oh product...

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

Is that right?
 
  • #4
Dick
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You used to have a (-a) in front of the first term. Where did that go? I liked it.
 
  • #5
Joza
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Ok, I mie be wrong here.

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

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

Correct?
 
  • #6
Dick
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Finally! Rest of the problem is easy, right?
 
  • #7
Joza
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I let it = 0 and solve to get values for x?
 
  • #8
Dick
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I think so. Correct me if I'm wrong. :smile:
 
  • #9
HallsofIvy
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Now, Dick, have you ever been wrong?
 
  • #10
Dick
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More times than I can count. I was betting on the Bears last night.
 

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