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Help for quickest and clearest route for differentiation question

  1. Aug 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the coordinates of the points on these curves at which the gradient has the given values.

    y=1/3x^(3/2)-x^(1/2), gradient=3/4


    3. The attempt at a solution

    Basically the problem I have isn't really finding the answer because.....

    x^(1/2)-x^-(1/2)=6/4[/b] and then from here I just used trial and error to find 4, but I want to know how I would follow it through with the algebra, i.e. only has x on one side as one term e.g. x= ans.


    Thanks in advance,

    kauymatty
     
  2. jcsd
  3. Aug 14, 2010 #2
    Try substituting z = x^(1/2), then cast the result into the form az^2 + bz + c = 0.
     
  4. Aug 14, 2010 #3

    vela

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    I'd square both sides of the equation. That'll eliminate the square roots completely.
     
  5. Aug 15, 2010 #4
    Thanks vela and banders, but after eliminating the roots I would still have the negative power, would I just get a common denominator by multiplying through with 16x as the denominator? (big of a noobish question XD)
     
  6. Aug 15, 2010 #5

    vela

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    Multiplying through by 16x would be fine.
     
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