(a) Find the slope of the tangent line to the parabola y = x^2 + 5x at the point (-1, –4) 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=\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a} provided that this limit exists. (ii) The expression of slope is m=\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-1, -4) until the parabola and the tangent line are indistinguishable.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9