(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I know one can find the critical points by taking whatever points make the first derivative zero or undefined. I also know that when you put the critical points into the second derivative the positivity or negativity of the number will tell you whether the graph will be concave up or down. What gets me is that the critical point you put into the 2nd derivative has a slope of zero. How can you find out the concavity from a point with a slope of zero?

2. Relevant equations

derivative properties, addition rule

3. The attempt at a solution

I have been thinking about this for awhile and it stumps me on why this way to find the concavity actually works.

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# Why 2nd derivative can find concavity

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