survey of calculus question

Question

Consider the following equation and point.

f(x) = 3x² − 9,    (−1, −6)

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

Answer 1

f(x) = 3x² - 9

f'(x) = 6x Slope of tangent line = f'(-1) = -6

Equation of tangent line is y - (-6) = -6[x - (-1)]

Simplify to get y = -6x - 12