3 An incomplete algorithm is specified in Fig. 3.
\(\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 2\)
Initial values: \(\mathrm { L } = 0 , \mathrm { R } = 2\).
Step 1 Compute \(\mathrm { M } = \frac { \mathrm { L } + \mathrm { R } } { 2 }\).
Step 2 Compute \(\mathrm { f } ( \mathrm { M } )\).
Step 3 If \(\mathrm { f } ( \mathrm { M } ) < 0\) change the value of L to that of M .
Otherwise change the value of \(R\) to that of \(M\).
Step 4 Go to Step 1. \section*{Fig. 3}

1. Apply two iterations of the algorithm.
2. After 10 iterations \(\mathrm { L } = 1.414063 , \mathrm { R } = 1.416016 , \mathrm { M } = 1.416016\) and \(\mathrm { f } ( \mathrm { M } ) = 0.005100\). Say what the algorithm achieves.
3. Say what is needed to complete the algorithm.