Explain why the existence of guarantees that exists.

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Explain why the existence of

f'(4)

guarantees that

\displaystyle \lim_{x\to 4} f(x)

exists.

Related theory

Derivative Foundations
Differentiability
Differentiability of functions
Continuity and Differentiability

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