The diagram presents a segment of the curve $y = \frac{8}{x} + 2x$ together with three points $A$, $B$ and $C$ on the curve, whose $x$-coordinates are $1$, $2$ and $5$ respectively.
(i)[4]
A point $P$ travels along the curve so that its $x$-coordinate is increasing steadily at $0.04$ units per second. Find the rate at which the $y$-coordinate of $P$ is changing as $P$ goes through $A$.
(ii)[6]
Find the volume generated when the shaded region is rotated through $360^\circ$ about the $x$-axis.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Finds $\dfrac{dy}{dx}$ by differentiating $y=\dfrac{8}{x}+2x$” …