Common Wisdom, Logarithmic Differentiation, and Compound Interest

Recently Michael RRed criticized the calculus curriculum for teaching how to differentiate functions of the form f (z)g() without providing any real applications [Reed 19871. Without endorsing Reed's sentiment, we present an everyday application of such a differentiation. The return on money invested at a given annual rate of interest varies with the frequency of compounding. Common wisdom says: The more frequent the compounding, the greater the return; and continuous compounding beats all. True, but texts do not prove these facts. They may carefully