CAIE P1 2016 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
TopicChain Rule

10 A curve has equation \(y = \mathrm { f } ( x )\) and it is given that \(\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { \frac { 1 } { 2 } } - 2 x ^ { - \frac { 1 } { 2 } }\). The point \(A\) is the only point on the curve at which the gradient is - 1 .
  1. Find the \(x\)-coordinate of \(A\).
  2. Given that the curve also passes through the point \(( 4,10 )\), find the \(y\)-coordinate of \(A\), giving your answer as a fraction.