Let f be the function that is differentiable on the open interval (-3,7). If f(0)=1, f(2)=−5, and f(6)=8, which of the following must be true?
a) f′(x)>0 for all x in (-3,7)
b) f′′(x)=0 for some x in (-3,7)
c) f′(c)=67​ for some c in (-3,7)
d) f(c)=0 for some c in (-3,7)