Let f be a differentiable function such that f'(x) ≥ 1 for all x. If a < b , which of the following statements could be false?

a. (f(b)-f(a))/b-a ≥ 1
b. f(b) > f(a)
c. There is a value c in the open interval (a,b) such that f(c)=0.
d. There is a value c in the open interval (a,b) such that f(c)= (f(a)+f(b))/2 .