Question

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

Answer 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)