CAIE P1 2017 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionJune
TopicStandard Integrals and Reverse Chain Rule

7 A curve for which \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 7 - x ^ { 2 } - 6 x\) passes through the point \(( 3 , - 10 )\).
  1. Find the equation of the curve.
  2. Express \(7 - x ^ { 2 } - 6 x\) in the form \(a - ( x + b ) ^ { 2 }\), where \(a\) and \(b\) are constants.
  3. Find the set of values of \(x\) for which the gradient of the curve is positive.