1.81: Differentiation, increments and a normal

0606/13/O/N/19 — Question 3 · 6 marks

(i)
Differentiate y=(3x2−1)−13y = (3x^{2} - 1)^{-\frac{1}{3}} with respect to xx.
[2]
(ii)
Find the approximate change in yy as xx increases from 3\sqrt{3} to 3+p\sqrt{3} + p, where pp is small.
[1]
(iii)
Find the equation of the normal to the curve y=(3x2−1)−13y = (3x^{2} - 1)^{-\frac{1}{3}} at the point where x=3x = \sqrt{3}.
[3]