2.2: Differentiation and stationary points of a rational function

0606/21/M/J/16 — Question 12 · 10 marks

A curve has equation y=2x−5x−1−12xy = \dfrac{2x - 5}{x - 1} - 12x.
(i)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[3]
(ii)
Find d2ydx2\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}}.
[2]
(iii)
Find the coordinates of the stationary points of the curve and determine their nature.
[5]