Continuity and differentiability.

Theorem 6.7.1   If $ f$ is differentiable at $ x_0$ , then $ f$ is continuous at $ x_0$ .

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Be careful! The converse is not true!}
For example, the absolute value function is continuous at 0, but certainly not differentiable at 0 (we proved this in Example 6.2; see also Figure 7).

Figure 5: The graph of the absolute value function.

Noah Dana-Picard 2007-12-28