The curve given by $y = 2x - 8x^{\frac{1}{2}}$ reaches a minimum at $A$ and cuts the positive $x$-axis at $B$.
(a)[4]
Find the coordinates for $A$ and $B$.
(b)[5]
The diagram depicts the curve with equation $y = 2x - 8x^{\frac{1}{2}}$ and the line $AB$. It is given that the equation of $AB$ is $y = \frac{2x - 32}{3}$. Find the area of the shaded region between the curve and the line.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate derivative $\frac{dy}{dx}=2-\tfrac12\times 8x^{-\frac{1}{2}}$” …