OCR C1 — Question 9

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicDifferentiation Applications
TypeFind normal line equation

9. A curve has the equation \(y = x ^ { 3 } - 5 x ^ { 2 } + 7 x\).
  1. Show that the curve only crosses the \(x\)-axis at one point. The point \(P\) on the curve has coordinates \(( 3,3 )\).
  2. Find an equation for the normal to the curve at \(P\), giving your answer in the form \(a x + b y = c\), where \(a , b\) and \(c\) are integers. The normal to the curve at \(P\) meets the coordinate axes at \(Q\) and \(R\).
  3. Show that triangle \(O Q R\), where \(O\) is the origin, has area \(28 \frac { 1 } { 8 }\).