Upon successful completion of Math& 151, the student should be able to:

1) Calculate or estimate limits of functions given by formulas, graphs, or tables; also using
properties of limits and L’hopital’s Rule.
2) State whether a function given by a graph or formula is continuous or differentiable at a
given point or on a given interval and justify your answer.
3) Calculate average and instantaneous rates of change in context, and state the meaning and
units of the derivative for functions given graphically.
4) Calculate derivatives of polynomial, rational, common transcendental functions,
combinations of these functions, and implicitly defined functions.
5) Apply the ideas and techniques of derivatives to
a) solve maximum and minimum problems
b) solve related rate problems,
c) calculate slopes and rates for function given as parametric equations (optional).
6) Find extreme values of modeling functions given by formulas or graphs:
a) predict, construct and interpret the shapes of graphs,
b) solve equations (i.e. Newton’s Method),
c) find linear approximations of functions (differentials).
7) Estimate a slope, a rate of change and the reasonableness of a result.
8) Restate in words the meanings of the solutions to applied problems, attaching the
appropriate units to an answer.
9) State which parts of a mathematical statement are assumptions (hypotheses) and which
parts are conclusions.