Activities

Getting Started

Day 1

Day 2

Day3

Final Project

Materials

Your Grade

Teacher's Corner

Activities

Day 1
The slope of a  line tells us how steep the line is--how fast or how slow the y value changes as we move along the graph from left to right.  We can use this same idea to talk about the slope of a curve.  Now, since a curve changes, the value of y will change a different rates, depending on where you are on the curve.  Go to the following animation to see an example of this idea.  Click the Back button when you are done. 

Curves are steeper in some places than in others. So, at any point on the curve, the slope of the curve will be the same as the slope of the tangent line at that spot.  With that in mind, watch the surfer again. His surf board is the tangent line. The surf board's steepness tells you the slope of the curve. Click the trace button and watch the slope value be traced out on the graph below. Click the Back button when you are done. 

Now let's see how to calculate the slope.  The first consideration is how will you know where to place a line so it's touching the curve at only one place.  As you'll see, you start with a secant line that goes through the point you are interested in.  Then move the other endpoint closer,...and closer...,and closer,....   Take a look. 

Click the Back button when you are done.

Now that you have considered the notion of the slope of a curve, let's see how to calculate specific values.  Get out paper and pencil.  You will go to the link below.  Select Book I, Chapter 3  The Derivative, Section 1  Slopes and Tangents, Module 1 Tangent Line Slope.  When you get to the problems, click on the help button.  Read through the text and the examples.  Add the process of calculating the slope of the curve to you notes.  Press the Problems button at the bottom of the page. Do problems 1-8. Work the problems until you get them all correct.  You will turn in a paper copy of the problems, the work that leads to your solution, and the correct answer.   

When you are done click the Back button repeatedly until you return to this page.