Problem #$8$: The graph of $z=f(x,y)$ is shown below. In each part, determine whether the given partial derivatives are

positive, negative, or zero. $($Note that the function is symmetric about $0$ in both the $x-$ and $y-$directions.$)$

$($a$)f_x(-2,-2)$ and $f_{}(-2,-2)$

$($b$)f_y(-2,-2)$ and $f_{yy}(-2,-2)$

$($c$)f_x(0,2)$ and $f_{}(0,2)$

$($d$)f_y(0,2)$ and $f_{yy}(0,2)$