CAIE P1 2022 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

8 The equation of a curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { \frac { 1 } { 2 } } - 3 x ^ { - \frac { 1 } { 2 } }\). The curve passes through the point \(( 3,5 )\).
  1. Find the equation of the curve.
  2. Find the \(x\)-coordinate of the stationary point.
  3. State the set of values of \(x\) for which \(y\) increases as \(x\) increases.