OCR C3 2009 June — Question 9

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2009
SessionJune
TopicProduct & Quotient Rules

9
  1. Show that, for all non-zero values of the constant \(k\), the curve $$y = \frac { k x ^ { 2 } - 1 } { k x ^ { 2 } + 1 }$$ has exactly one stationary point.
  2. Show that, for all non-zero values of the constant \(m\), the curve $$y = \mathrm { e } ^ { m x } \left( x ^ { 2 } + m x \right)$$ has exactly two stationary points.