In order to find what concavity it is changing from and to, you plug in numbers on either side of the inflection point. if the result is negative, the graph is concave down and if it is

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## How do I tell concavity from the first derivative?

Use the first derivative test and the results of step 2 to determine whether [latex]f[/latex] has a local maximum, a local minimum, or neither at each of the critical points. Recall from Chapter 4.3 that when talking about local extrema, the value of the extremum is the y value and the location of the extremum is the x value.

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## Concavity review (article)

When a function is concave upward, its first derivative is increasing. If a function is concave downward, however, in a particular interval, it means that the tangents to its graph all lie above

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