Golden-Section Search Numerical Method

Function for finding the x optimum to make f(x) extreme, using the golden-section search method

% Inputs: with examples
% stO = maximum or minimum string: stO = 'minimum';
% AF = anonymous function equation: AF = @(x) 1-((20^2)./(9.81*(((3*x)+((x.^2)/2)).^3))).*(3+x);
% xb = initial guess x bracket = [xL xU], where xL = lower boundary x and xU = upper boundary x: xb = [0 2.5];
% ed = desired approximate relative error = (2-phi)*|(xU - xL)/xO|, where phi =(1+5^0.5)/2: ed = 0.01;
% Outputs
% xO = x optimum
% errO = approximate relative error
% nO = number of iterations
% xOV = x optimum vector
% errOV = approximate relative error vector
% AFD1 = anonymous function 1st derivative
% AFD2 = anonymous function 2nd derivative