Class Summary for July 1, 1998

MAC 2311--Calculus I

 
 
We continued working on the class file class0629.mws from last time, looking at the last two examples on antiderivatives of scalar-valued functions. These work the same as before: in fact, they are actually easier, since we only have one component to work with instead of two. We did use one of the examples to note an important distinction: that change in position is not the same as distance travelled. If there is a change in direction, then the net difference between the starting and ending positions may not represent the total distance traveled. We have to look more carefully and consider if there is a change (or several changes) in direction; each of these switches represents a relative extreme value of the position, and we have to sum the distances traveled between each successive pair of these points to arrive at the total distance. We find these extreme points by making use of the fact that at each of these the velocity is zero. (Note: we didn't discuss this issue for vector-valued functions--there it is a bit more complicated).

Next, we began looking at the derivative from a graphical perspective. We did an exercise in class where we took several functions of differnt kinds, and for each we plotted the function and its first two derivatives on the same axes. From looking at these, we deduced (induced, actually) some general relationships between the graph of a function and its derivative (and its second derivative). From these general principles, we should be able to sketch the derivative or antiderivative of a function, given its graph--we will do this next time. We introduced informally several terms during the course of this (concave up/down, relative extrema, increasing/decreasing), which we will make more precise next time. We will also construct a table summarizing the key relationships between the graph of a function and the graphs of its first and second derivatives.
 

Distributions:

Assignment:

 
©1998 All rights reserved. This is not an official FGCU Web page.
Page created 1 July 1998, last updated 1 July 1998