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Help for quickest and clearest route for differentiation question

  • Thread starter kauymatty
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  • #1
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Homework Statement


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


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
 

Answers and Replies

  • #2
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Try substituting z = x^(1/2), then cast the result into the form az^2 + bz + c = 0.
 
  • #3
vela
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I'd square both sides of the equation. That'll eliminate the square roots completely.
 
  • #4
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I'd square both sides of the equation. That'll eliminate the square roots completely.
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)
 
  • #5
vela
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Multiplying through by 16x would be fine.
 

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