Edexcel FP1 2012 June — Question 6

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJune
TopicSign Change & Interval Methods
TypeLinear Interpolation Only

6. $$f ( x ) = \tan \left( \frac { x } { 2 } \right) + 3 x - 6 , \quad - \pi < x < \pi$$
  1. Show that the equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval \([ 1,2 ]\).
  2. Use linear interpolation once on the interval \([ 1,2 ]\) to find an approximation to \(\alpha\). Give your answer to 2 decimal places.