4.2 Section Summary

We have seen in this section that the second derivative gives us additional information about the graph of a function. Specifically, positive and negative values of the second derivative tell us where the graph is concave up or concave down, respectively. If `t` is a critical value of `f` and the graph is concave up at the corresponding point on the graph, that point must be a local minimum point. If `t` is a critical value and the graph is concave down, the point must be a local maximum. Where the second derivative is `0`, there may be an inflection point. If the second derivative changes sign, then this point is an inflection point.