Given a function, 𝑓 (𝑥), its difference quotient tells us the slope of the line that passes through two points of the curve: (𝑎, 𝑓 (𝑎)) and ((𝑎 + ℎ), 𝑓 (𝑎 + ℎ)). Let’s visualize this to better understand the concept of the difference quotient.
This is the Difference Quotient: f (x+x) f (x)x. It gives the average slope between two points on a curve f (x) that are x apart:
This video gives the formula for the difference quotient (aka, the subtraction fraction) and does a couple examples of finding it for different functions. Show Video Lesson