Calculus need help

Question

1. Use limit definition to find  for the function, . Show detailed work

Answer 1

[f(x+h) - f(x)]/h = [3(x+h)² - 4(x+h) + 1 - 3x² + 4x - 1] / h

= [3x² + 6xh + 3h² -4x - 4h + 1 - 3x² + 4x - 1] / h = (6xh + 3h² - 4h) / h = 6x + 3h - 4

f'(x) = the limit of the expression above as h approaches zero = 6x - 4

So, f'(2) = 6(2) - 4 = 8.