A twice-differentiable function g satisfies g(−2)=g(2). Which of the following conclusions must be true?
a) There exists a number c in (−2,2) such that g′′(c)=0.
b) There exists a number c in (−2,2) such that g(c)=0.
c) There exists a number c in (−2,2) such that g′(c)=0.
d) g′(0)=0.