An axiomatic development of the derivative and the antiderivative is presented. (DT)

Properties of solids generated by the rotation of some of the well-known solids about given axes are discussed. (DT)

Examples are given of difficulties that students have in determining extrema of real-valued functions of real variables. (DT)

Pure and applied mathematical research is discussed briefly. The author gives an example of mathematical research on functional differential equations that was motivated by a student error on a calculus examination. (MK)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)