The curve is described by $y = \frac{1}{2}(4x - 3)^{-1}$. Point $A$ on the curve has coordinates $(1, \frac{1}{2})$.
(i(a))[5]
Determine and simplify the equation of the normal at $A$.
(a)[5]
Work out and simplify the normal’s equation through $A$.
(b)[3]
Find the $x$-coordinate of the point where this normal cuts the curve again.
(ii)[2]
A point moves along the curve so that, as it passes through $A$, its $x$-coordinate is decreasing at $0.3$ units per second. Determine the rate at which its $y$-coordinate changes at $A$.
Worked solution & mark scheme
This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: “After differentiating, $\frac{dy}{dx}=-\frac{1}{2}(4x-3)^{-2}\cdot4$” …