The curve $y = 2x^2$ is drawn with the points $X(-2,0)$ and $P(p,0)$ marked on it. Point $Q$ is on the curve, and $PQ$ is parallel to the $y$-axis.
(i)[2]
Express the area, $A$, of triangle $XPQ$ in terms of $p$.
(ii)[3]
As $P$ travels along the $x$-axis at a steady rate of $0.02$ units per second, $Q$ moves on the curve so that $PQ$ stays parallel to the $y$-axis. Find the rate at which $A$ is increasing when $p = 2$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Area found by applying $\tfrac12 bh$ with both base and height written in terms of $p$” …