Definition of the Derivative – Unit 2

This is a re-post and update of the second in a series of posts from last year. It contains links to posts on this blog about the definition of the derivative for your reference in planning. Other updated post on the 2019 CED will come throughout the year, hopefully, a few weeks before you get…

Local Linearity

If you use your calculator or graphing program and zoom-in of the graph of a function (with equal zoom factors in both directions), the graph eventually looks like a line: the graph appears to be straight. This property is called Local Linearity. The slope of this line is the number called the derivative. (There are exceptions:…

Seeing Difference Quotients

Third in the graphing calculator series.  In working up to the definition of the derivative you probably mention difference quotients. They are The forward difference quotient (FDQ):  The backwards difference quotient (BDQ): , and The symmetric difference quotient (SDQ):  Each of these is the slope of a (different) secant line and the limit of each as…

Determining the Indeterminate

When determining the limit of an expression the first step is to substitute the value the independent variable approaches into the expression. If a real number results, you are all set; that number is the limit. When you do not get a real number often expression is one of the several indeterminate forms listed below:…