Given the unconstrained function:

$f(z_1,z_2)=3z_1+\frac{1}{z_1-1}+z_2^2+\frac{1}{z_2}$

a$)$ Calculate the gradient of $f$ and the direction of steepest descent, $d^{(0)},$ at $z^{(0)}={\left[\begin{array}{cc}3& 0\mathrm{.}5\end{array}\right]}^T.$

b$)$ Using the direction of steepest descent calculated in part $($a$),$ update the design using the standard

formula:

$z^{(1)}=z^{(0)}+d^{(0)}$

Here, you should write $z^{(1)}$ as a symbolic function of $.$ Use Matlab to evaluate $()=$

$f(z^{(0)}+d^{(0)})$ for $$ ranging between $0$ and $1$ and plot the curve of $()$ versus $.$ Keep in mind

that, when plotting, you may need to adjust the limits of the $y$ axis using y im $([$ymin ymax $]).$

Use Matlab's help to learn about the ylim command.