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Optimization: find zeros of a derivative

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the maximum point of P(h)=-10h+4410-(6800/h)


    2. Relevant equations
    P(h)=-10h+4410-(6800/h)

    3. The attempt at a solution
    P(h)=-10h+4410-(6800/h)
    P'(h)=-10+(6800/h^2)
    P'(0)=-10h^2+6800
    10h^2=6800
    Divide both sides by 10:
    h^2=680
    and sqrt both sides:
    h=26.1
     
  2. jcsd
  3. May 8, 2013 #2

    Dick

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    h=sqrt(680) isn't the only root, there's also h=(-sqrt(680)). Or are you only considering h>0? You'll still want to consider what happens near h=0. What's your question?
     
  4. May 8, 2013 #3
    Oops sorry.. My question is how do you isolate h from P'(h)=-10+(6800/h^2)
    I know the correct answer is h=82.5 but I'm not sure how to get there. I know that the sqrt of 6800 is 82.5 but then what happens with the -10?
     
  5. May 8, 2013 #4

    Dick

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    If you are trying to solve 0=-10+(6800/h^2) to find a point where the derivative equals 0 then I think you already did it correctly. That means 10=6800/h^2 so 10h^2=6800, h^2=680. The derivative isn't 0 at h=82.5. That's wrong.
     
  6. May 8, 2013 #5
    Okay thank you!! The answer that was given was my teacher's answer and I was going crazy trying to figure out what I was doing wrong.
     
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