Inverses

This series of posts reviews and expands what students know from pre-calculus about inverses. This leads to finding the derivative of exponential functions, ax, and the definition of e, from which comes the definition of the natural logarithm. Inverses Graphically and Numerically The Range of the Inverse The Calculus of Inverses The Derivatives of Exponential Functions…

My Favorite Function

My favorite function is . I like to ask folks how many zeros this function has on the interval . Most folks will get their calculator out and graph the function on the interval Two zeros: one at 1 and the other about 0.05 more or less. So then I suggest they look at .…

Logarithms

Students first encounter logarithms in Algebra 2 or their last pre-calculus course. They are usually defined as exponents and their properties “proven” by reference to the corresponding properties of exponents. This is good enough at the time, but in calculus we are ready to define logarithms properly. The result is the definition in terms of…