For the curve, $\frac{dy}{dx} = 2 - 8(3x + 4)^{-\frac{1}{2}}$.
(i)[2]
Point $P$ travels along the curve so that its $x$-coordinate rises at a steady rate of $0.3$ units per second. Determine how fast the $y$-coordinate is changing when $P$ crosses the $y$-axis.
(ii)[4]
At the point where the curve meets the $y$-axis, $y = \frac{4}{3}$. Determine the equation of the curve.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiating gives $\frac{dy}{dx}=2-8(3x+4)^{-3/2}$.” …