Which one of the following conditions must hold at a point x=c for a piece-wise defined function f to be differentiable at c?
a) Only f(c−)=f(c+)
b) Only f′(c−)=f′(c+)
c) Both f(c−)=f(c+) and f′(c−)=f′(c+)
d) f(c−)=f(c+) and at least one of f′(c−) or f′(c+) exists