A function is known to be differentiable at .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A function gg is known to be differentiable at x=2x=2. (a) State the limit definition of the derivative g′(2)g'(2). (b) Using appropriate reasoning based on the definition in part (a), determine whether gg must be continuous at x=2x=2. Provide a clear justification for your conclusion.

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