Implicit Differentiation and Inverses

Implicit differentiation of relations is done using the Chain Rule.  Implicit Differentiation (from last Friday’s post. I discovered I never did a post on this topic before!) Implicit differentiation of parametric equations A Vector’s Derivative The inverse series  This series of posts reviews and expands what students know from pre-calculus about inverses. This leads to…

Good Question 9

This is a good question that leads to other good questions, both mathematical and philosophical. A few days ago this question was posted on a private Facebook page for AP Calculus Readers. The problem and illustration were photographed from an un-cited textbook. Player 1 runs to first base [from home plate] at a speed of…

February 2016

As I hope you’ve noticed there is a new pull-down on the navigation bar called “Website.” For some years I’ve had a website at linmcmullin.net that lately I’ve been neglecting. I decided to close it in the next few days, and therefore, I move most of the material that is there to this new tab. The…

January 2016

HAPPY NEW YEAR – a few more days off and then back to school! If you haven’t already, it is time to start integration. The posts on starting integration were listed in December since I try to stay ahead of things so you’ll have time to prepare. With that in mind here are past posts…

A Vector’s Derivatives

A question on the AP Calculus Community bulletin board this past Sunday inspired me to write this brief outline of what the derivatives of parametric equations mean and where they come from. The Position Equation or Position Vector A parametric equation gives the coordinates of points (x, y) in the plane as functions of a…

Roulettes and Art – 2

Continuing with our discussion of ways to produce interesting designs with the Roulette Generator (RG) for Winplot, Here are some hints on making more detailed designs using more than one function. Hint #5: Adding more graphs to the first: You may add other graphs by selecting the roulette and/or velocity equations from the Inventory (CTRL+I)…