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**alreadyinuse** Find concavity:

1. Find the second derivative and set it equal to zero. This will give you your inflection points.

2. Using those inflection points, find your intervals. For example, if a second derivative gave the inflection points 0 and 2, the intervals would be: -infinity < x < 0, 0 < x < 2, and 2 < x < infinity.

3. Choose a point for each of the intervals. Plug it into the second derivative. Greater than zero means it concaves upward, less than zero = downward.

I don't know if that was helpful or not, but that's pretty much it step-by-step.