Difference Quotients

Difference Quotients!

The purpose of finding a difference quotient is to find the instantaneous slope at a point on a curve. This is done by finding the slope.  In detail:

• Consider two values along the x-axis, x and x+h, where h is the distance between the two points.  The smaller h is, the more exact the difference quotient will be.

• Calculate the slope of the line passing between the points A: (x, f(x)), and B: ((x+h), f(x+h)).

• Simplify

This is the difference quotient, and can be used for any values of x and x+h.

 Here's an Example:

 And then you get to learn limits, but shhh, we won't tell Mr. Bruns...

 This has been just a glimpse at difference quotients... more to come at the end of the year! Yay! but no spoilers...

Blog post by Erin J