A contour diagram for the smooth function $\backslash ($ z$=$f$($x$,$ y$)\backslash )$ is given in the figure below.

$($a$)$ Is $\backslash ($ z $\backslash )$ an increasing or a decreasing function of $\backslash ($ x $\backslash )?$

$($b$)$ Is $\backslash ($ z $\backslash )$ an increasing or a decreasing function of $\backslash ($ y $\backslash )?$

$($c$)$ Is $\backslash ($ f$\_\{$x x$\}\backslash )$ positive or negative?

$($d$)$ Is $\backslash ($ f$\_\{$y y$\}\backslash )$ positive or negative?

$($e$)$ Is $\backslash ($

abla f $\backslash )$ longer at point P or Q $?$

$($f$)$ If you were to sketch $\backslash ($

abla f $\backslash )$ on the contour diagram at the point Q $,$ how would it appear? Select all that apply.

A$.$ Parallel to the x $-$axis

B$.$ Perpendicular to the contour at point Q $.$

C$.$ Points in the direction of increasing contour values.

D$.$ Tangent to the contour at point Q $.$

E$.$ Parallel to the y$-$axis.

F$.$ Points in the direction of decreasing contour values. E$.$ Parallel to the $\backslash ($ y $\backslash )-$axis.

F$.$ Points in the direction of decreasing contour values.

$($Click on graph to enlarge$)$