OCR C1 — Question 9

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicDifferentiation Applications
TypeFind stationary points

9. The curve \(C\) has the equation $$y = 3 - x ^ { \frac { 1 } { 2 } } - 2 x ^ { - \frac { 1 } { 2 } } , \quad x > 0 .$$
  1. Find the coordinates of the points where \(C\) crosses the \(x\)-axis.
  2. Find the exact coordinates of the stationary point of \(C\).
  3. Determine the nature of the stationary point.
  4. Sketch the curve \(C\).