3.58: Derivative, small change and stationary point

0606/22/O/N/24 — Question 2 · 8 marks

Variables xx and yy are related by y=x+2xy = x + \dfrac{2}{x}.
(a)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[3]
(b)
When y=12y = 12, x=4x = 4. Find the approximate change in xx when yy increases from 1212 by 0.060.06.
[3]
(c)
Find the xx-coordinate of the stationary point on y=x+2xy = x + \dfrac{2}{x}.
[2]