For a differentiable function f, which of the following statements must be true?
a) If f attains a local maximum at x=c, then f′(c)=0.
b) If f′(c)=0, then f has an inflection point at x=c.
c) If f′(x)>0 on an open interval, then f′′(x)>0 on that interval.
d) If f attains a local maximum at x=c, then f′′(c)<0.