The diagram presents a segment of the curve with equation $y = (3x + 4)^{\tfrac{1}{2}}$ together with the tangent to the curve at point $A$. The $x$-coordinate of $A$ is $4$.
(i)[5]
Find the equation of the tangent to the curve at $A$.
(ii)[5]
Find, showing all necessary working, the area of the shaded region.
(iii)[3]
A point moves along the curve. At point $P$, the $y$-coordinate is rising at half the speed at which the $x$-coordinate is rising. Find the $x$-coordinate of $P$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Derivative found correctly using chain rule” …