April 14th, 2015, 08:50 AM  #1 
Newbie Joined: Feb 2015 From: Scotland Posts: 20 Thanks: 0  Differentiation
Hi All, I'm a bit stuck with this and any help would be appreciated... h(x) = sqrt(x^25) Determine the coordinates of the points where the tangent to the curve h(x) has gradient 3/2 I differentiated and got x/sqrt(x^25). First of all, is this correct? Second, if this x/sqrt(x^25) = 3/2 how do you solve it? I always have trouble with x when it's in a fraction. I tried x= 3(sqrt(x^25))/2 but got stuck again with the half power on (x^25). 
April 14th, 2015, 08:55 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,978 Thanks: 1573 
your derivative is correct $\displaystyle \frac{x}{\sqrt{x^25}} = \frac{3}{2} \implies x < 0$ $\displaystyle 2x = 3\sqrt{x^25}$ $\displaystyle 4x^2 = 9(x^25)$ $\displaystyle x = 3$ 
April 14th, 2015, 08:58 AM  #3 
Newbie Joined: Feb 2015 From: Scotland Posts: 20 Thanks: 0 
Wow, thanks. You make it look so easy. I had times it by two but missed squaring everything.


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