Question $04$: Given $y=f(x)=-2x^6-1\mathrm{.}5x^4+10x+2.$

Use a root$-$location technique to determine the maximum of this function $($i$.$e$.,$ the value of $y$ corresponding to the $x$ value for which $d\frac{y}{d}x=0).$ Perform iterations until the approximate relative error falls below $0\mathrm{.}005\%.$ If you use a bracketing method, use initial guesses of $xl=0$ and $xu=1.$ If you use the Newton$-$Raphson or the fixed$-$point iteration method, use an initial guess of $x(1)=1.$ If you use the Secant method, use initial guesses of $x(1)=0$ and $x(2)=1.$ Assuming that convergence is not an issue, choose the technique that is best suited to this problem. Justify your choice.

Deliverables: MATLAB Script file $($s$)$