A curve is given by the equation $y = 2 + \frac{3}{2x - 1}$.
(i)[2]
Obtain an expression for $\frac{dy}{dx}$.
(ii)[1]
Explain why the curve has no stationary points.
(iii)[4]
At the point $P$ on the curve, $x = 2$. Show that the normal to the curve at $P$ passes through the origin.
(iv)[2]
A point moves along the curve so that its $x$-coordinate is decreasing at a constant rate of $0.06$ units per second. Find the rate of change of the $y$-coordinate as the point passes through $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiates correctly to $\frac{dy}{dx}=-\frac{3}{(2x-1)^2}$, with an unsimplified equivalent also allowed.” …