Math 22 Concavity and the Second-Derivative Test

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Formal Definition of Concavity

 Let  $f$  be differentiable on an open interval  $I$ . The graph of  $f$  is
 1. Concave upward on  $I$  when  $f'(x)$  is increasing on the interval.
 2. Concave downward on  $I$  when  $f'(x)$  is decreasing on the interval.

=Test for Concavity

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