1.1. The profile of the first part of the Big Delta rollercoaster is modelled using the function $f(x)=xsin(\frac{1}{2}x).$  The graph of  $h=f(x),x\geq0,$  is shown below.

h is the height, in metres of a person sat on the rollercoaster.
h = 0 is the height at which passengers board the rollercoaster.

x is the horizontal distance travelled, in metres, measured from the starting point.

Explain why the Newton-Raphson method would fail should it be used to attempt to find the horizontal distance travelled when a passenger on the Big Delta is at the point marked P on the graph.

1.2. Show that$f'(x)=\frac{1}{2}xcos(\frac{1}{2}x)+sin(\frac{1}{2}x).$

1.3. Use the Newton-Raphson method with initial value ${x}_{0}=14$ to find the horizontal distance travelled the first time Big Delta reaches a height of 10 metres above its starting point. Give your answer to three significant figures.

1.4. Confirm your answer to part (c) is correct to three significant figures.