Steepest descent vs$.$ others

Write a program for minimizing a function in two variables using the Steepest descent method $($which you must lookup$).$ Minimize the function

$f(x,y)=0\mathrm{.}1(12+x^2+\frac{1+x^2}{x^2}+\frac{100+x^2{y}^2}{x^4{y}^4})$

using steepest descent, Newton$-$Raphson, BFGS$,$ and Nelder$-$Mead simplex starting from the same initial guess. Report $x^{**}$ and the CPU time as a table. Explain your results.