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Difference Quotient Rule
Let's get familiar with a rule that is very similar to the average rate of change formula.
The rule is known as the Difference Quotient Rule.
The Difference Quotient is used to calculate the slope of the SECANT line between two points on the graph of a function.
Our goal is to find the slope of the secant line.
Looking at the image below, notice that one point is identified as (x, f(x)) and the other point as ((x + h), f(x + h)). I know, you are wondering why "h"? "h" represents the distance between x and the other point on the function's graph.
If x = 3 and the distance between 3 and the other point is 4, the second point would be x = 7.
Because we are placing a point somewhere on the function's graph, we will represent that second point as x + h.
"h" changes as we get closer and closer to a point P, so we can determine the slope of the tangent line at point P.
This is where limits come in - and that will be something you will experience next year in Calc!
Right now, we will work on becoming comfortable using the difference quotient rule, so you know how to apply it next year.
Two versions of the Difference Quotient rule
There are two versions of the difference quotient rule.
Each formula computes the slope of the secant line through two points on the graph of f(x).
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