Nov 2010 p11 q11
1087
The equation of a curve is \(y = \frac{9}{2-x}\).
Find an expression for \(\frac{dy}{dx}\) and determine, with a reason, whether the curve has any stationary points.
Solution
Given \(y = \frac{9}{2-x}\), we can rewrite it as \(y = 9(2-x)^{-1}\).
Using the chain rule, \(\frac{dy}{dx} = -9(2-x)^{-2} \times (-1)\).
This simplifies to \(\frac{dy}{dx} = \frac{9}{(2-x)^2}\).
For stationary points, \(\frac{dy}{dx} = 0\). However, \(\frac{9}{(2-x)^2} \neq 0\) for any real \(x\), so there are no stationary points.
Log in to record attempts.