1.10: Stationary points of a rational curve

4PM1/1/June/2021 — Question 7 · 11 marks

The curve C\displaystyle C has equation
y=xx2+4.y=\frac{x}{x^2+4}.
(a) Using calculus, find the coordinates of the stationary points on C\displaystyle C.
(5)
(b) Show that
d2ydx2=2x(x2−12)(x2+4)3.\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=\frac{2x(x^2-12)}{(x^2+4)^3}.
(4)
(c) Hence, or otherwise, determine the nature of each of these stationary points.
(2)