Consider the function in the picture:$$

Write Python Code Solutions please.$$

$1)$ Apply the steepest gradient descent method starting at initial point $($x$,$ y$)=(0\mathrm{.}1,0\mathrm{.}1)$ with step size $0\mathrm{.}01.($i$)$ What happens to the sequence of points and the gradient of f at those points?

$2)$ Apply the steepest gradient descent method starting at initial point $($x$,$ y$)=(0\mathrm{.}1,0\mathrm{.}1)$ with step size $0\mathrm{.}01.($i$)$ What happens to the sequence of points and the gradient of f at those points? If the sequence does not converge, examine points from the initial part of

the sequence only.

Use the Newton$$s method instead of the steepest gradient descent. Discuss how the sequence of points behave differently when the Newton$$s method is used.