Question

What is the total change of f(x), if f'(x) = 2x - 3x^2, over the interval [0, 3]?

Answer 1

if f ' (x) = 2x- 3x^2
f(x) = x^2 - x^3 + c

f(0) = 0-0+c
f(3) = 9 + 27 + c = 36+c

change from f(0) to f(3)
= 36+c - c
= 36

Answer 2

My only options are:

-12
6
-18
-6

Answer 3

Oops. Flipped a minus sign

f(3) = 9-27+c = -18+c

total change is thus -18