Question $3$ Starting at the point $(0,2,0),$ I walk up the hill z $=4$ x$2$ y$2.$

The projection of my path on the xy plane is the line y $=2$x $2.$

$($a$)$ At what point on my path is my altitude $($the z$-$value$)$ the greatest?

$($b$)$ What is the slope m of my path $($taking the z$-$axis to be vertical$)$ when I

am at the point $(1,0,3)?[$Hint: Parametrize my path $($take x to

be t$).]$