• Aug 17th 2011, 03:15 AM
jonoe
a - ( (b) / (c+x^2) )

The line goes through (2,$\displaystyle 2/3$) and the gradient of the curve is at its maximum at x= root6/3 (square root of 6 divided by 3)

Prove a = 1, b = 2, c = 2.

Can I please have a detailed solution to this? I've tried so many ways, been hours already. It was in the dydx and integration section.
• Aug 17th 2011, 04:06 AM
jonoe
Re: Help!
sorry c wasnt 3, c = 2
• Aug 17th 2011, 04:13 AM
Siron
Re: Help!
For example, if the curve goes throught the point $\displaystyle \left(2,\frac{2}{3}\right)$ that means:
$\displaystyle \frac{2}{3}=a-\frac{b}{c+4}$

Have you tried something this way? Also with the other given information? ...
• Aug 17th 2011, 04:16 AM
jonoe
Re: Help!
Yes I was aware it was a curve. I've tried something like that. Still ended up with 2 unknowns. and 3 in the other.

And the point where the gradient is its max. Stuck on how to get that equation. Or use that info. Would it be double derivative?
• Aug 17th 2011, 04:29 AM
Siron
Re: Help!
Yes, calculate the second derivative of the function, then let $\displaystyle f''(x)=0$ and enter $\displaystyle x=\frac{\sqrt{6}}{3}$ therefore you can calculate $\displaystyle c$.