Edexcel C12 2017 January — Question 9

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2017
SessionJanuary
TopicDifferentiation Applications
TypeFind stationary points

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f39ade34-32e2-4b5c-b80a-9663c6a65c87-14_609_744_223_593} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where $$f ( x ) = \frac { 8 } { x } + \frac { 1 } { 2 } x - 5 , \quad 0 < x \leqslant 12$$ The curve crosses the \(x\)-axis at \(( 2,0 )\) and \(( 8,0 )\) and has a minimum point at \(A\).
  1. Use calculus to find the coordinates of point \(A\).
  2. State
    1. the roots of the equation \(2 \mathrm { f } ( x ) = 0\)
    2. the coordinates of the turning point on the curve \(y = \mathrm { f } ( x ) + 2\)
    3. the roots of the equation \(\mathrm { f } ( 4 x ) = 0\)