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Two global theorems.
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Differentiable functions.
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One-sided derivative at one
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Continuity and differentiability.
Theorem
6
.
7
.
1
If
is differentiable at
, then
is continuous at
.
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