This document provides an overview of concavity, inflection points, and how to find the local extrema of functions. It explains that a graph is concave up when tangent slopes are increasing and concave down when slopes are decreasing. An inflection point is where the direction of concavity changes and occurs when the second derivative is zero or undefined, though one must check the signs of the second derivative on either side. It gives examples of finding the inflection points of f(x)=x^4+2x^3-1 and using the second derivative test to find local extrema of f(x)=x^2e^x, and provides practice problems from the textbook.