A curve goes through the point $A(4,6)$ and satisfies $\frac{dy}{dx} = 1 + 2x^{-\frac{1}{2}}$. A point $P$ moves along the curve so that the $x$-coordinate of $P$ is rising at a constant rate of $3$ units per minute.
(a)[3]
Find the rate at which the $y$-coordinate of $P$ is increasing when $P$ is at $A$.
(b)[3]
Find the equation of the curve.
(c)[5]
The tangent to the curve at $A$ crosses the $x$-axis at $B$ and the normal to the curve at $A$ crosses the $x$-axis at $C$. Find the area of triangle $ABC$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Evaluate $\frac{dy}{dx}=2$ when $x=4$” …