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…

Implicit Differentiation

I’ve never liked memorizing formulas. I would rather know where they came from or be able to tie it to something I already know. One of my least favorite formulas to remember and explain was the formula for the second derivative of a curve given in parametric form. No longer. If  and, then the tradition…

Foreshadowing the Chain Rule

I assigned another very easy but good problem this week. It was simple enough, but it gave a hint of things to come. Use the Product Rule to find the derivative of . Since we have not yet discussed the Chain Rule, the Product Rule was the only way to go.  And likewise for higher…