Suppose you want lim x-> a   [f(x) - f(a)](x-a) where a = 2


get [f(x) - f(a)](x-a) with a = 2, then take the limit as x -> 2
f(x) - f(a)/(x-a) =( 4.5x^2 -3x + 2 - (4.5(2)^2 - 3(2) + 2)]/(x- 2)

= (4.5x^2 - 3x + 2 - 14)/(x-2)
= (4.5x^2 -3x -12)/(x-2)
= (4.5x + 6)(x-2)/(x-2)
= 4.5x + 6

Now we take lim x-> 2 (4.5x + 6) = 4.5(2) + 6 = 15