For each statement below, determine if the statement is true, false, or if the statement cannot be evaluated.?

Question

A.f(0)>f(1) B. f(2)>f(1) C.f(1)>f(3)
f'(x)=(x-1)^2 and f(x) contains the origin.

Answer 1

Integrating the last relation gives
f(x) = (x-1)³ /3 + C
Since f(x) contains the origin
0 = -1/3+C
f(x) = [(x-1)³ +1] / 3.
So
f(0) = 0, f(1) = 1/3, so statement A is false.
f(2) = 2/3, f(1) = 1/3, so statement B is true.
f(3) = 3, f(1) = 1/3, so statement C is false.

Answer 2

Because f'(x) = "something squared",
f'(x) is non-negative and f(x) is monotoneously increasing.

For this reason f(0)