Consider the function $f(x,y,z)=e^{x}yz$ in Question $6.$ Answer each of the following:

$($i$)$ Find the rate of change of the function at $(0,1,2)$ towards the point $(3,2,-1).$

$($ii$)$ Find the direction and the magnitude of the maximum rate of change of the function at $(0,1,2).$

If $f(x,y)=2x^2+3x-y^2+y-4,$ find the stationary points and classify them.

Maximize the function $f(x,y,z)=xyz$ subject to the condition $x^2+y^2+z^2=3$