CAIE P3 2011 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2011
SessionJune
TopicDifferential equations

6 A certain curve is such that its gradient at a point \(( x , y )\) is proportional to \(x y\). At the point \(( 1,2 )\) the gradient is 4 .
  1. By setting up and solving a differential equation, show that the equation of the curve is \(y = 2 \mathrm { e } ^ { x ^ { 2 } - 1 }\).
  2. State the gradient of the curve at the point \(( - 1,2 )\) and sketch the curve.