CAIE P1 2012 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicDifferential equations

9 A curve is such that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = - 4 x\). The curve has a maximum point at (2,12).
  1. Find the equation of the curve. A point \(P\) moves along the curve in such a way that the \(x\)-coordinate is increasing at 0.05 units per second.
  2. Find the rate at which the \(y\)-coordinate is changing when \(x = 3\), stating whether the \(y\)-coordinate is increasing or decreasing.