Upon successful completion of the course, students will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and L'Hopial's Rule; state whether a function given by a graph or formula is continuous or differentiable at at given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, and common transcendental functions, compositions thereof, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems and calculate slopes and rates for functions given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using Newton's method; find linear approximations to functions using differentials; verbally restate the meanings of the solutions to applied problems, attaching the appropriate units to the answers; state which parts of a mathematical statement are assumptions, such as hypotheses and which parts are conclusions; find anti-derivatives by changing variables and using tables; and calculate definite integrals.