Consider the following function:

Question

f(x) = x³ + 8,    (−2, 0)

(a) Find an equation of the tangent line to the graph of f at the given point.

y= ?

(b) Use a graphing utility to graph the function and its tangent line at the point.

Answer 1

Hey Shannon,

f(x) = x³ + 8, (-2, 0)

a)

First, find the derivative of f(x). f'(x) = 3x² (power rule)

Then plug in x = -2 into f'(x) to find the slope of the tangent line at x = -2. f'(-2) = 12.

Now we know x-value, y-value, and the slope of the line. x = -2, y = 0, m = 12

Plugging in you will get, 0 = 12 * (- 2) + b. Thus, b = 24.

Therefore, the equation for the tangent line at (- 2, 0) is y = 12x + 24.

b) I believe you can do this on your graphing calculator.