3.73: Product rule derivative and stationary point

0606/11/M/J/23 — Question 8 · 7 marks

(a)
A curve has equation y=(2x−1)1/3(3x+4)−1y=(2x-1)^{1/3}(3x+4)^{-1}. Show that
dydx=(2x−1)−2/3(Ax+B)(3x+4)2\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{(2x-1)^{-2/3}(Ax+B)}{(3x+4)^{2}}
where AA and BB are integers to be found.
[5]
(b)
Find the coordinates of the stationary point on the curve.
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