CAIE P1 2014 June — Question 12

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionJune
TopicStandard Integrals and Reverse Chain Rule

12 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { \frac { 1 } { 2 } } - x ^ { - \frac { 1 } { 2 } }\). The curve passes through the point \(\left( 4 , \frac { 2 } { 3 } \right)\).
  1. Find the equation of the curve.
  2. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  3. Find the coordinates of the stationary point and determine its nature.