Let f(x) = x^3 - x^2 + x - 1. Find an equation for tangent line to f at x = 2.

Answer 1

x=2 could be rewritten as (2,0)

Look at example 1:
http://www.cliffsnotes.com/study_guide/Tangent-and-Normal-Lines.topicArticleId-39909,articleId-39887.html

Answer 2

f(x) = x^3 - x^2 + x - 1
f'(x) = 3x^2 - 2x + 1

when x=2 , f'(1) = 12 - 4 + 1 = 9
also when x=2, f(2) = 8 - 4 + 2 -1 = 5

so the tangent has a slope of 9 and passes through (2,5)

equation of tangent is y = 9x + b
at (2.5)
5 = 9(2) + b
b = -13

equation of tangent: y = 9x - 13