Using the gradient descent method to optimize the following functions in the range of $2,2$ with the initial point $x_0=[1\mathrm{.}51\mathrm{.}5].$

$f(x,y)=x^2+x+y+2*y^2$

a$.$ Choose the stop criteria as

where $f_{t-1}$ and $f_i$ represent the values at $t+1$ and $t$ steps.

b$.$ Choose leaming rate: $0\mathrm{.}1,$ get the final solution $(x)$ which is the coordinate $x,y$ when the algorithm stop. Plot the trajectory of $x($all $x$ from $x0$ to $x)$ together with the $f(x,y)$ in the same figure which is similar as follows