CAIE P1 2019 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
TopicIntegration by Substitution

9 A curve for which \(\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x - 1 ) ^ { \frac { 1 } { 2 } } - 2\) passes through the point ( 2,3 ).
  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 on the curve and, showing all necessary working, determine the nature of this stationary point.