2.74: Differentiation of a product with a surd

0606/23/O/N/18 — Question 10 · 9 marks

The equation of a curve is y=x23+xy = x^{2}\sqrt{3 + x} for x≥−3x \ge -3.
(i)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}.
[3]
(ii)
Find the equation of the tangent to the curve y=x23+xy = x^{2}\sqrt{3 + x} at the point where x=1x = 1.
[3]
(iii)
Find the coordinates of the turning points of the curve y=x23+xy = x^{2}\sqrt{3 + x}.
[4]