We discuss how to find and evaluate local extrema of a function using derivatives.

We develop the Extreme Value Theorem, a way to know when an absolute extrema must exist without doing calculus.

We discuss how to find and evaluate absolute extrema of a function using derivatives.

We present the visual interpretation of concavity and how it is determined by the second derivative.

We discuss how to determine where a function is concave up or concave down.

We discuss the real world and visual interpretation of a point of inflection.

We discuss how to find points of inflection of a function using the second derivative.

We discuss how to use the second derivative to classify extrema of a function.

We discuss one of the original uses for calculus, how position, velocity, and acceleration are related.

We discuss how to use our tools to create detailed sketches of functions beyond the ability of precalc tools.

We discuss how to visualize linear approximation as a tangent line application.

We discuss to actually apply linear approximation to approximate a value.

We discuss how to solve real world style problems that involve interrelated rates of change.

We discuss how to model and then optimize that model, for real world style problems.