Edexcel C1 2013 January — Question 11

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2013
SessionJanuary
TopicDifferentiation Applications
TypeFind derivative of polynomial

11. The curve \(C\) has equation $$y = 2 x - 8 \sqrt { } x + 5 , \quad x \geqslant 0$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving each term in its simplest form. The point \(P\) on \(C\) has \(x\)-coordinate equal to \(\frac { 1 } { 4 }\)
  2. Find the equation of the tangent to \(C\) at the point \(P\), giving your answer in the form \(y = a x + b\), where \(a\) and \(b\) are constants. The tangent to \(C\) at the point \(Q\) is parallel to the line with equation \(2 x - 3 y + 18 = 0\)
  3. Find the coordinates of \(Q\).