Math 006 - Introduction to Calculus

Lecture 4

New Stuff

This class is taken from chapter 2 of the text book. We will cover the following topics in this class:

• Applications of derivatives Finding the equation for a tangent to a curve. Examples involving motion, eg velocity, accelleration. Related rates.

We may also still be finishing going over rules for derivatives, continued from week 3.

Main Part of class

We will go over the rules of finding derivatives again, and look at various applications, for instance, finding the slope of a tangent line:

There is an "opposite" kind of question we'll also cover; for the above, we know the point where we want to find the slope of the tangent, and we use that to find the slope (and then the equation for the line); but we could start off knowing the slope, and find the point where the tangent has that slope:

I do not intend to cover much new material this lecture; I will go over the rules for finding derivatives, introduced at the end of last lecture, and give examples. Also we will go over some of the homework questions and quiz two after the break. If you didn't do well in the homework or quizzes, you can ask questions and get the ideas clarrified. The midterm will consist of questions similar to those on the quizzes and homeworks, so you should make sure you understand this material.

Tutorial and Examples

The following questions from the text book should be done for practice, but are not to be handed in for marking.

• Ex 2.2 Page 83, B.Ex 2.f,h. Ex 7, 8
• Ex 2.3 Page 88, B.Ex 3.c, Ex 7, 8
• Ex 2.4 Page 92, B.Ex 3.e, 4
• Ex 2.5 Page 95, B.Ex 1, 6
• Ex 2.6 Page 102, B.Ex 1.a,c,i, Ex 3, Ex 7.

The following questions from the text book should be handed in Wednesday February 18. 1. Find the derivatives of the following functions:

• f(x) = (x² + 1) (x² - 1)
• f(x) = (x³ + 3)^1/2
• f(x) = (x² + 5x +1)/(x²+1)
• f(x) = (x² + 2)²(x-1)

Handout

Please send corrections to spelling mistakes, and any other comments, to me.