(a)[3]
Determine the coordinates of the curve's minimum point for $y = \frac{9}{4}x^2 - 12x + 18$.
(b)[5]
The diagram displays the curves with equations $y = \frac{9}{4}x^2 - 12x + 18$ and $y = 18 - \frac{3}{8}x^2$. They meet at the points $(0, 18)$ and $(4, 6)$. Find the area of the shaded region.
(c)[3]
A point $P$ moves along the curve $y = 18 - \frac{3}{8}x^2$ so that the $x$-coordinate of $P$ rises at a constant rate of $2$ units per second. Find the rate at which the $y$-coordinate of $P$ is changing when $x = 4$.