The diagram represents the curve $y = (6x + 2)^{\frac{1}{3}}$ and the point $A(1, 2)$, which is on the curve. At $A$, the tangent meets the $y$-axis at $B$, while the normal meets the $x$-axis at $C$.
(a(i))[5]
Find the equation of the tangent $AB$ and the equation of the normal $AC$.
(a(ii))[3]
Find the distance $BC$.
(a(iii))[4]
Find the coordinates of the point of intersection, $E$, of $OA$ and $BC$, and determine whether $E$ is the mid-point of $OA$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiation gives $\frac{dy}{dx}=6\times\frac13(6x+2)^{-2/3}$” …