CAIE P1 2021 June — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicDifferentiation from First Principles

3 The equation of a curve is \(y = ( x - 3 ) \sqrt { x + 1 } + 3\). The following points lie on the curve. Non-exact values are rounded to 4 decimal places. $$A ( 2 , k ) \quad B ( 2.9,2.8025 ) \quad C ( 2.99,2.9800 ) \quad D ( 2.999,2.9980 ) \quad E ( 3,3 )$$
  1. Find \(k\), giving your answer correct to 4 decimal places.
  2. Find the gradient of \(A E\), giving your answer correct to 4 decimal places.
    The gradients of \(B E , C E\) and \(D E\), rounded to 4 decimal places, are 1.9748, 1.9975 and 1.9997 respectively.
  3. State, giving a reason for your answer, what the values of the four gradients suggest about the gradient of the curve at the point \(E\).