OCR C1 2016 June — Question 8

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2016
SessionJune
TopicDifferentiation from First Principles

8 A curve has equation \(y = 2 x ^ { 2 }\). The points \(A\) and \(B\) lie on the curve and have \(x\)-coordinates 5 and \(5 + h\) respectively, where \(h > 0\).
  1. Show that the gradient of the line \(A B\) is \(20 + 2 h\).
  2. Explain how the answer to part (i) relates to the gradient of the curve at \(A\).
  3. The normal to the curve at \(A\) meets the \(y\)-axis at the point \(C\). Find the \(y\)-coordinate of \(C\).