Problem

The equation of a curve is $y = 4x^2 + \frac{9}{x^2} - 8$.

(a) A point $P$ is moving along the curve in such a way that its $y$-coordinate is decreasing at 5 units per second.

Find the rate at which the $x$-coordinate of point $P$ is changing when $x = 2$.

(b) Find the coordinates of the stationary points of the curve and determine their nature.