Problem

The equation of a curve is $y=\frac{8}{3x-8}-\frac{6}{x-1}$.

(a) Find the coordinates of the point at which the tangent to the curve at the point $(3,5)$ intersects the line $y=-8x$.

(b) (i) Find the $x$-coordinates of each of the stationary points of the curve.

(ii) Find $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$ and hence determine the nature of each of the stationary points.