CAIE P1 2018 November — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionNovember
TopicConnected Rates of Change

10 A curve has equation \(y = \frac { 1 } { 2 } ( 4 x - 3 ) ^ { - 1 }\). The point \(A\) on the curve has coordinates \(\left( 1 , \frac { 1 } { 2 } \right)\).
  1. (a) Find and simplify the equation of the normal through \(A\).
    (b) Find the \(x\)-coordinate of the point where this normal meets the curve again.
  2. A point is moving along the curve in such a way that as it passes through \(A\) its \(x\)-coordinate is decreasing at the rate of 0.3 units per second. Find the rate of change of its \(y\)-coordinate at \(A\).