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Local maximum point

  1. Feb 4, 2007 #1
    Local maximum point......

    1. The problem statement, all variables and given/known data

    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.


    3. 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.
     
  2. jcsd
  3. Feb 4, 2007 #2

    Dick

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    Your derivative is wrong. Remember the product rule?
     
  4. Feb 4, 2007 #3
    Oh product.........

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

    Is that right?
     
  5. Feb 4, 2007 #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.
     
  6. Feb 4, 2007 #5
    Ok, I mie be wrong here.

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

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

    Correct?
     
  7. Feb 4, 2007 #6

    Dick

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    Finally! Rest of the problem is easy, right?
     
  8. Feb 4, 2007 #7
    I let it = 0 and solve to get values for x?
     
  9. Feb 4, 2007 #8

    Dick

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    I think so. Correct me if I'm wrong. :smile:
     
  10. Feb 5, 2007 #9

    HallsofIvy

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    Now, Dick, have you ever been wrong?
     
  11. Feb 5, 2007 #10

    Dick

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