The diagram depicts part of the curve $y = \frac{9}{2x+3}$, which cuts the $y$-axis at $B(0, 3)$. On the curve, the point $A$ has coordinates $(3, 1)$, and the tangent drawn at $A$ meets the $y$-axis at $C$.
(i)[4]
Find the equation of the tangent at $A$.
(ii)[1]
Determine, showing all necessary working, whether $C$ lies nearer to $B$ or to $O$.
(iii)[4]
Find, showing all necessary working, the exact volume obtained when the shaded region is rotated through $360^\circ$ about the $x$-axis.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carries out differentiation on $y=\frac{9}{2x+3}$” …