CAIE P1 2003 November — Question 4

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2003
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

4 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - 4 x + 1\). The curve passes through the point \(( 1,5 )\).
  1. Find the equation of the curve.
  2. Find the set of values of \(x\) for which the gradient of the curve is positive.