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Derivative = 0

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data

    I need to solve for x by setting the derivative of A equal to 0.
    A=(x^2)/2(x-2)

    3. The attempt at a solution

    dA/dx= x(x-2)^-1(-1)((1/2)x^2)

    = (-x^3)/2(x-2)

    If someone could check this so far and point me in the right direction, that would be great.
     
  2. jcsd
  3. Sep 8, 2009 #2

    arildno

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    Re: derivative=0

    Learn the rules of differentiation, this is just nonsense.
     
  4. Sep 8, 2009 #3

    lurflurf

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    Re: derivative=0

    does
    A=(x^2)/2(x-2)
    mean
    A=(x^2)/[2(x-2)]
    ?
    If so
    A=(x^2)/[2(x-2)]=A=(x^2-2)/[2(x-2)]+2/[2(x-2)]=(x+2)/2+1/(x-2))
     
  5. Sep 8, 2009 #4
    Re: derivative=0

    Sorry, I've looked back and realize that it was really confusing.
    Here is a more comprehensible restatement.

    A=(x^2)/[2(x-2)]

    Is the derivative of A (-x^3)/[2(x-2)],
    or did I do something completely wrong?
     
  6. Sep 8, 2009 #5

    arildno

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    Re: derivative=0

    Yes, it is utterly wrong.

    A(x) is a fraction!

    We may write it as:

    [tex]A(x)=\frac{f(x)}{g(x)}[/tex]

    1. Exercise: What is f(x)?
    2. Exercise: What is g(x)?

    Furthermore, the derivative of a fraction is given as:
    [tex]A'(x)=\frac{f'(x)*g(x)-f(x)*g'(x)}{g(x)^{2}}(*)[/tex]

    3. Exercise: What is f'(x)?
    4. Exercise: What is g'(x)?

    5. Put the correct expressions into (*), and simplify the expression for A'(x)!
     
  7. Sep 8, 2009 #6

    lurflurf

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    Re: derivative=0

    hint simplify A
    A=(x^2)/[2(x-2)]=(x^2-2)/[2(x-2)]+2/[2(x-2)]=(x+2)/2+1/(x-2)
     
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