$(60$ points$)$ a$)$ Use the golden$-$section search to determine the length of the shortest ladder that reaches from the ground over a $3m$ high fence to touch the building's wall, as shown in the figure below. You know that the length cannot be lower than $5m$ and higher than $9m.$ Use a stopping criterion of $5\%.$

b$)$ Use MATLAB's fminbnd to solve the same problem. Make sure to show the records of all iterations.