StellarConcavity describes how the slope of a function is changing. A function is concave up on an interval if its derivative is increasing there, which is equivalent to f''(x)>0. A function is concave down on an interval if its derivative is decreasing there, which is equivalent to f''(x)<0. Geometrically, a graph that is concave up looks like it bends upward, while a graph that is concave down looks like it bends downward. The second derivative is the main tool for studying this behavior.
To determine concavity, students compute the second derivative, find where it is zero or undefined, and use those points to divide the domain into intervals. Then they test the sign of f''(x) on each interval. Concavity is important because it gives a deeper description of the graph than increasing or decreasing alone. It also leads directly to the study of inflection points, where concavity changes, in the next part of the unit.