AQA C1 2005 January — Question 2

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2005
SessionJanuary
TopicDifferentiation Applications
TypeFind normal line equation

2 A curve has equation \(y = x ^ { 5 } - 6 x ^ { 3 } - 3 x + 25\).
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  2. The point \(P\) on the curve has coordinates \(( 2,3 )\).
    1. Show that the gradient of the curve at \(P\) is 5 .
    2. Hence find an equation of the normal to the curve at \(P\), expressing your answer in the form \(a x + b y = c\), where \(a , b\) and \(c\) are integers.
  3. Determine whether \(y\) is increasing or decreasing when \(x = 1\).