Which of the following statements correctly describes the relationship between…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Which of the following statements correctly describes the relationship between continuity and differentiability of a function f at a point x=c?
(a) If f is continuous at c, then f must be differentiable at c.
(b) If f is differentiable at c, then f must be continuous at c.
(c) If f is not continuous at c, then f can still be differentiable at c.
(d) Continuity and differentiability are independent; neither property implies the other at c.