Consider the function in the picture:$$

Write Python Code Solutions:

Apply the steepest gradient descent method starting at the initial point $($x$,$ y$)=(2\mathrm{.}2,-2\mathrm{.}2).$

$($i$)$ What happens to the sequence of points and the gradient of f at those points?

$($ii$)$ Repeat the steepest gradient descent method, but starting at various different initial points around $(2,-2)$ and confirm your finding does not depend on the choice of initial point.

Use the Newton$$s method instead of the steepest gradient descent. Compare the rate of convergence of the steepest gradient descent and Newton$$s methods.