CAIE P1 2021 March — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionMarch
TopicStandard Integrals and Reverse Chain Rule

6 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 } { ( 3 x - 2 ) ^ { 3 } }\) and \(A ( 1 , - 3 )\) lies on the curve. A point is moving along the curve and at \(A\) the \(y\)-coordinate of the point is increasing at 3 units per second.
  1. Find the rate of increase at \(A\) of the \(x\)-coordinate of the point.
  2. Find the equation of the curve.