OCR MEI C2 2007 January — Question 5

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
TopicDifferentiation from First Principles

5 A is the point \(( 2,1 )\) on the curve \(y = \frac { 4 } { x ^ { 2 } }\).
B is the point on the same curve with \(x\)-coordinate 2.1.
  1. Calculate the gradient of the chord AB of the curve. Give your answer correct to 2 decimal places.
  2. Give the \(x\)-coordinate of a point C on the curve for which the gradient of chord AC is a better approximation to the gradient of the curve at A .
  3. Use calculus to find the gradient of the curve at A .