CAIE P1 2021 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionNovember
TopicProduct & Quotient Rules

10 The function f is defined by \(\mathrm { f } ( x ) = x ^ { 2 } + \frac { k } { x } + 2\) for \(x > 0\).
  1. Given that the curve with equation \(y = \mathrm { f } ( x )\) has a stationary point when \(x = 2\), find \(k\).
  2. Determine the nature of the stationary point.
  3. Given that this is the only stationary point of the curve, find the range of f .