Continuity and differentiability.

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

\begin{figure}\mbox{\subfigure{\epsfig{file=error.eps, height=1cm}} \qquad
Be careful! The converse is not true!}
\end{figure}
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.
\begin{figure}\mbox{\epsfig{file=AbsoluteValue.eps,height=4cm}}\end{figure}



Noah Dana-Picard 2007-12-28