CAIE P1 2021 June — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicChain Rule

11 The gradient of a curve is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 ( 3 x - 5 ) ^ { 3 } - k x ^ { 2 }\), where \(k\) is a constant. The curve has a stationary point at \(( 2 , - 3.5 )\).
  1. Find the value of \(k\).
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  2. Find the equation of the curve.
  3. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
  4. Determine the nature of the stationary point at \(( 2 , - 3.5 )\).