Find f. f '' (x) = - 2 + 36x - 12x2, f (0) = 8, f ' (0) = 18 f (x) =

Integrate f '' (x) = - 2 + 36x - 12x2 with respect to x:

f ' (x) = - 2x + (36/2) x^2 - (12/3) x^3 + c. Find c by letting x = 0 and using f (0) = 8.

Then f ' (0) = - 2x + 18x^2 - 4x^3 + c = 18 (which was given).

Then - 0 + 0 - 0 + c = 18, so c = 18 and

f ' (x) = - 2x + 18x^2 - 4x^3 + 18.

Go through the same integration process to find f (x).