$y=-\frac{w}{48EI}(2x^4-3L{x}^3+L^{3}x)$

For this beam, assume:

$L=600cm,E=58,000k\frac{N}{c}{m}^2,I=32,000c{m}^4,w=5\mathrm{.}5k\frac{N}{c}m$

Use an anonymous function to create the deflection equation.

Use the golden$-$section search method to determine the number of iterations it will take to find minimum of the function with an error that is less than $0\mathrm{.}05\%.$ Use initial guesses of $0$ and $L.$ Store the optimal value for each iteration in the xopt variable.

Plot the deflection equation to confirm that your solution is accurate

Calculate the approximate error for each iteration using the equation ${}_a=(2-)|\frac{x_u-x_l}{x_{\text{o}\text{p}\text{t}}}|x100$ where, phi is the golden ration, $x_u$ and $x_{\text{I}}$ are the current bounds, and x$\_$opt is your current estimate of the optimal value.

On the same graph, plot both the optimal value and the error with respect to the iterations to identify when the solution effectively converges. Note: use the function yyaxis to get two independent vertical axes. Using matlab code