Graph 8-11-15

Tangents and Slopes

Using the function to learn about its derivative.  In this post we will look at a way of helping students discover the numerical and graphical properties of the derivative and how they can be determined from the graph of the function. These ideas can be used very early, when you are first relating the function…

Figure 2

Discovering the Derivative

Discovering the Derivative with a Graphing Calculator This is an outline of how to introduce the idea that the slope of the line tangent to a graph can be found, or at least approximated, by finding the slope of a line through two very close points in the graph.  It is a set of graphing calculator…

Power Rule Implies Chain Rule

Having developed the Product Rule  and the Power Rule  for derivatives in your class, you can explore similar rules for the product of more than two functions and suddenly the Chain Rule will appear. For three functions use the associative property of multiplication with the rule above: So expanding with a slight change in notation: For…

Table MVT

Mean Tables

The AP calculus exams always seem to have a multiple-choice table question in which the stem describes function in words and students are asked which of 5 tables could be a table of values for the function.  Could be because you can never be sure without other information what happens between values in the table.…

Jean Gaston Darboux
1842 - 1917

Darboux’s Theorem

Jean Gaston Darboux was a French mathematician who lived from 1842 to 1917. Of his several important theorems the one we will consider says that the derivative of a function has the Intermediate Value Theorem property – that is, the derivative takes on all the values between the values of the derivative at the endpoints…