1.56: Stationary point of a product with a square root

0606/12/O/N/20 — Question 9 · 8 marks

1.56 diagram
A curve has equation y=(2x−1)4x+3y = (2x - 1)\sqrt{4x + 3}.
(a)
Show that dydx=4(Ax+B)4x+3\dfrac{\mathrm{d}y}{\mathrm{d}x} = \dfrac{4(Ax + B)}{\sqrt{4x + 3}}, where AA and BB are constants.
[5]
(b)
Hence write down the xx-coordinate of the stationary point of the curve.
[1]
(c)
Determine the nature of this stationary point.
[2]