Determine f' (2) for f (x) = (x^2 - 2x) (3x-1)

f (x) = (x^2 - 2x) (3x-1) is a product and is most easily differentiated using the product rule:

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

Now subst. 2 for x in this equation. We get:

f ' (2) = (2^2 - 2 (2)) * 3 + (3 (2) - 1) (2 (2) - 2), or

=3 (4-4) + (6-1) (2) so f ' (2) = 10 (answer)