Let g:R→R be a non constant twice differentiable such that g′(21)=g′(23). If a real valued function f is defined as f(x)= 21 [g(x)+g(2−x)], then
A. f′′(x)=0 for atleast two x in (0,2)
B. f ′′(x)=0 for exactly one x in (0,1)
C. f ′′(x)=0 for no x in (0,1)
D. f′(3/2)+f′(1/2)=1