Which of the following statements best describes the relationship between continuity…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Which of the following statements best describes the relationship between continuity and differentiability of a function f at a point x=c?
(a) If f is continuous at x=c, then f must also be differentiable at x=c.
(b) If f is not differentiable at x=c, then f must be discontinuous at x=c.
(c) If f is differentiable at x=c, then f must be continuous at x=c.
(d) Continuity and differentiability at x=c are independent; knowing one gives no information about the other.