OCR C1 — Question 10

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicCurve Sketching
TypeFind stationary points of polynomial

10. The curve with equation \(y = ( 2 - x ) ( 3 - x ) ^ { 2 }\) crosses the \(x\)-axis at the point \(A\) and touches the \(x\)-axis at the point \(B\).
  1. Sketch the curve, showing the coordinates of \(A\) and \(B\).
  2. Show that the tangent to the curve at \(A\) has the equation $$x + y = 2$$ Given that the curve is stationary at the points \(B\) and \(C\),
  3. find the exact coordinates of \(C\).