Finer grained standards that are part of this one
Model rates of change, including related rates problems.
Find points of inflection of functions. Understand the relationship between the concavity of f and the sign of f". Understand points of inflection as places where concavity changes.
Decide where functions are decreasing and increasing. Understand the relationship between the increasing and decreasing behavior of f and the sign of f'.
Use first and second derivatives to help sketch graphs modeling real-world and other mathematical problems with and without technology. Compare the corresponding characteristics of the graphs of f, f', and f".
Find a tangent line to a curve at a point and a local linear approximation.
Find the velocity and acceleration of a particle moving in a straight line.
Find the slope of a curve at a point, including points at which there are vertical tangents and no tangents.
Solve optimization real-world problems with and without technology.
Analyze real-world problems modeled by curves, including the notions of monotonicity and concavity with and without technology.
Use implicit differentiation to find the derivative of an inverse function.