Consider the parabola y $=8$x $$ x$2.$

$($a$)$ Find the slope m of the tangent line to the parabola at the point $(1,7).$

$($i$)$ using this definition: The tangent line to the curve

y $=$ f$($x$)$

at the point

P$($a$,$ f$($a$))$

is the line through P with slope

m $=$lim$$x $$ a$$

f$($x$)$ f$($a$)$x $$ a

provided that this limit exists.