The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.


Introduction

In Section 1.2 the slope of the line through the points (x1, y1) and (x2, y2) is shown to be the ratio of the change in y to the change in x,

slope = 01_real_and_hyperreal_numbers-75.gif

If the line has the equation

y = mx + b,

then the constant m is the slope.

What is meant by the slope of a curve? The differential calculus is needed to answer this question, as well as to provide a method of computing the value of the slope. We shall do this in the next chapter. However, to provide motivation, we now describe intuitively the method of finding the slope.

Consider the parabola

y = x2.

The slope will measure the direction of a curve just as it measures the direction of a line. The slope of this curve will be different at different points on the x-axis, because the direction of the curve changes.


Last Update: 2006-11-15