Which one of the following conditions must hold at a point for a piece-wise defined…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
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