For the function $\backslash ($ f$($x$)=($x$-1)^\{4\}-$x$+2$ e$^\{$x$\}\backslash$quad $\backslash )($one$-$dimensional optimization problem $-$ same function with question $1),$ write a matlab code to find the local minimum$/$minimums of the function by using, $(20$ pts$.)$

a$)$ Nelder and Mead $($Simplex$)$ Method. $(8$ pts$.)$

b$)$ Hooke$-$Jeeves Pattern Search Method. $(8$ pts$.)$

c$)$ Compare the performances of these two methods $($create a table and show the number of iterations and optimum solution$).$ Determine which one is faster and explain your result. $(4$ pts$.)$