http://www.ck12.org Chapter 14. Concepts of Calculus
14.8 Instantaneous Rate of Change
Here you will learn about instantaneous rate of change and the concept of a derivative.
When you first learned about slope you learned the mnemonic device “rise over run” to help you remember that to
calculate the slope between two points you use the following formula:
m=yx^22 −−yx 11In Calculus, you learn that for curved functions, it makes more sense to discuss the slope at one precise point rather
than between two points. The slope at one point is called the slope of the tangent line and the slope between two
separate points is called a secant line.
Consider a car driving down the highway and think about its speed. You are probably thinking about speed in terms
of going a given distance in a given amount of time. The units could be miles per hour or feet per second, but the
units always have time in the denominator. What happens when you consider the instantaneous speed of the car at
one instant of time? Wouldn’t the denominator be zero?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/63172http://www.youtube.com/watch?v=7CvLzpzGhJI Brightstorm: Definition of a Derivative
Guidance
The slope at a pointP(also called the slope of the tangent line) can be approximated by the slope of secant lines as
the “run” of each secant line approaches zero.