The diagram shows a section of the curve with equation $y = x^{\frac{1}{2}} + k^2 x^{-\frac{1}{2}}$, where $k$ is a positive constant.
(a)[4]
Find the coordinates of the minimum point on the curve, giving your answer in terms of $k$.
(b)[4]
The tangent at the point on the curve where $x = 4k^2$ meets the $y$-axis at $P$. Find the $y$-coordinate of $P$ in terms of $k$.
(c)[3]
The shaded region is enclosed by the curve, the $x$-axis and the lines $x = \frac{9}{4}k^2$ and $x = 4k^2$. Find the area of the shaded region in terms of $k$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiates accurately to obtain $\frac{dy}{dx}$” …