Additional Mathematics 0606 / Straight-line graphs / 3.573.57: Differentiate y=(3x2−2)2/3/(x−1)y=(3x^{2}-2)^{2/3}/(x-1)y=(3x2−2)2/3/(x−1)0606/13/O/N/22 — Question 12 · 7 marksMark as done · Save for later · Show all solutionsIt is given that y=(3x2−2)23x−1y = \dfrac{(3x^{2} - 2)^{\frac{2}{3}}}{x - 1}y=x−1(3x2−2)32, for x>1x > 1x>1.(a)Write dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}dxdy in the form (3x2−2)−13(x−1)2(x2+Ax+B)\dfrac{(3x^{2} - 2)^{-\frac{1}{3}}}{(x - 1)^{2}}(x^{2} + Ax + B)(x−1)2(3x2−2)−31(x2+Ax+B), where AAA and BBB are integers.[5]▸ Answer(b)Find the approximate increase in yyy as xxx increases from 222 to 2+p2 + p2+p, where ppp is small.[2]▸ Answer▸ Official mark scheme← 3.55: Linear law: y3y^{3}y3 against lnx\ln xlnx3.58: Perpendicular bisector of PQPQPQ; points R,SR,SR,S →
