Question 10 - A-Level Maths

Exam Board	OCR
Module	C1 (Core Mathematics 1)
Year	2005
Session	June
Topic	Differentiation Applications
Type	Find stationary points

Given that \(y = \frac { 1 } { 3 } x ^ { 3 } - 9 x\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
Find the coordinates of the stationary points on the curve \(y = \frac { 1 } { 3 } x ^ { 3 } - 9 x\).
Determine whether each stationary point is a maximum point or a minimum point.
Given that \(24 x + 3 y + 2 = 0\) is the equation of the tangent to the curve at the point ( \(p , q\) ), find \(p\) and \(q\).