OCR FP2 2015 June — Question 8

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2015
SessionJune
TopicHyperbolic functions

8 It is given that \(\mathrm { f } ( x ) = 2 \sinh x + 3 \cosh x\).
  1. Show that the curve \(y = \mathrm { f } ( x )\) has a stationary point at \(x = - \frac { 1 } { 2 } \ln 5\) and find the value of \(y\) at this point.
  2. Solve the equation \(\mathrm { f } ( x ) = 5\), giving your answers exactly. \section*{Question 9 begins on page 4.}