Question 2 - A-Level Maths

Exam Board	OCR
Module	Mechanics 1 (Mechanics 1)
Year	2018
Session	September
Topic	Differentiation Applications
Type	Find stationary points

2 A curve has equation \(y = a x ^ { 4 } + b x ^ { 3 } - 2 x + 3\).

Given that the curve has a stationary point where \(x = 2\), show that \(16 a + 6 b = 1\).
Given also that this stationary point is a point of inflection, determine the values of \(a\) and \(b\).