# Math 22 Concavity and the Second-Derivative Test

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