The function minimisation problem can be stated: given a continuous function $f(x),$ find a point $x^{***}$ such that $f(x^{***})$ is a minimum

value of $f.$ The image below depicts a possible scenario. The aim is to seek $x^{***}$ from repeated evaluations, $f(x_1),f(x_2),f(x_3)dots$

Suppose the answer lies in the known interval $a,b$ : the end points $a,b$ are said to bracket the solution. The idea behind a

bracketing algorithm is to shrink $a,b$ until a satisfactory answer is obtained.

Describe a bracketing algorithm that attempts to solve the minimisation problem.

You should describe your idea in words $(6$ marks$)$ and provide pseudocode $(4$ marks$).$