Edexcel C1 2013 June — Question 10

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2013
SessionJune
TopicIntegration by Substitution

10. A curve has equation \(y = \mathrm { f } ( x )\). The point \(P\) with coordinates \(( 9,0 )\) lies on the curve. Given that $$\mathrm { f } ^ { \prime } ( x ) = \frac { x + 9 } { \sqrt { } x } , \quad x > 0$$
  1. find \(\mathrm { f } ( x )\).
  2. Find the \(x\)-coordinates of the two points on \(y = \mathrm { f } ( x )\) where the gradient of the curve is equal to 10