How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
How to use the optimization methods of calculus to optimize cost or revenue.
How to define the derivative function f'(x).
How to compute the average rate of change of the amount of a drug in a patient's bloodstream over an interval of time, and how to interpret whether the amount is increasing or decreasing over time.
How to determine the derivative of a power function.
How to compute the derivative of a polynomial function using two properties of the derivative.
How to use the definition of the derivative to find a derivative formula for exponential functions.
How to determine the derivative of a linear function.
How to recognize and use Newton's and Leibniz's notation for the derivative.
How to infer the derivative of the natural log function using a calculator investigation.
How to define the derivative of a function at a point x=a.
How to derive the quadratic formula by completing the square.
How to evaluate the limit of a function using continuity.
How to find an antiderivative of a function.
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.
How to define an antiderivative.
How to solve simple differential equations.