5.
$$f ( x ) = 3 \sqrt { } x + \frac { 18 } { \sqrt { } x } - 20$$
- Show that the equation \(\mathrm { f } ( x ) = 0\) has a root \(\alpha\) in the interval \([ 1.1,1.2 ]\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
- Using \(x _ { 0 } = 1.1\) as a first approximation to \(\alpha\), apply the Newton-Raphson procedure once to \(\mathrm { f } ( x )\) to find a second approximation to \(\alpha\), giving your answer to 3 significant figures.