# Help for quickest and clearest route for differentiation question

1. Aug 14, 2010

### kauymatty

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.

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.

kauymatty

2. Aug 14, 2010

### BAnders1

Try substituting z = x^(1/2), then cast the result into the form az^2 + bz + c = 0.

3. Aug 14, 2010

### vela

Staff Emeritus
I'd square both sides of the equation. That'll eliminate the square roots completely.

4. Aug 15, 2010

### kauymatty

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. Aug 15, 2010

### vela

Staff Emeritus
Multiplying through by 16x would be fine.