$[-/2$ Points$]$

SCALCET$9$M $2\mathrm{.}7\mathrm{.}003.$

$($a$)$ Find the slope of the tangent line to the parabola $y=x^2+7x$ at the point $(-3,-12)$ by using the following parameters.

$($i$)$ The tangent line to the curve $y=f(x)$ at the point $P(a,f(a))$ is the line through $P$ with slope $m=\underset{xa}{lim}\frac{f(x)-f(a)}{x-a}$ provided that this limit exists.

$m=$

$$

$($ii$)$ The expression of slope is $m=\underset{h0}{lim}\frac{f(a+h)-f(a)}{h}.$

$m=$

$$

$($b$)$ Find an equation of the tangent line in part $($a$).$

$y=$

$$

$($c$)$ Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $(-3,-12)$ until the parabola and the tangent line are indistinguishable.