1.70: Differentiation, stationary point and its nature

0606/13/M/J/20 — Question 10 · 10 marks

(a)
Given that y=xx+2y = x\sqrt{x + 2}, show that dydx=Ax+B2x+2\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{Ax + B}{2\sqrt{x + 2}}, where AA and BB are constants.
[5]
(b)
Find the exact coordinates of the stationary point of the curve y=xx+2y = x\sqrt{x + 2}.
[3]
(c)
Determine the nature of this stationary point.
[2]