For the function f(x)=(x+8)^2, find the equation of the tangent line to the graph of f at x=-2. if the equation of the tangent line is written as...

We'll write the equation of the tangent line
as:

y - f(-2) = m[x - (-2)]
(1)

m is the slope of the tangent line and it represents
the tangent line to the graph of the function f(x) = (x+8)^2, for x =
-2.

m = f'(-2)

For the
beginning, we'll calculate f'(x):

f'(x) =
2(x+8)

Now, we'll determine
f'(-2):

f'(-2) =
2*(-2+8)

f'(-2) = 12

We'll
calculate  the value of the function for x = -2:

f(-2) =
(-2+8)^2

f(-2) = 36

Now, we'll
substitute the found values into the equation (1):

y - 36 =
12(x+2)

We'll add 36 both
sides:

y = 12(x+2) + 36

We'll
remove the brackets:

y = 12x + 24 +
36

y = 12x +
60

The equation of the tangent line is: y =
12x + 60