What is the Difference Quotient? (and How to Find It) | Functions, Rate of Change, Calculus

What is the difference quotient? Today we go over where it comes from, how to find it, and more! We've got examples and a practice problem, it'll be a blast! If we want to know a function's average rate of change over some distance, we will end up using a difference quotient whether we know it or not. At least we will if we do it right! We go over that process in the video lesson! Slopes, rates of change, secant lines, and more, all show up in today's lesson! And this has a very strong relation to the beginnings of calculus as well. If you haven't started studying calculus, you will see this again when you do! What happens if h gets closer and closer to 0 in the difference quotient? Just something to think on! The practice problem was to find the difference quotient of 3x^2 + 4x - 2. In the numerator we have 3(x+h)^2 + 4(x+h) - 2. We expand and simplify, then divide by h, and that gives us 3h + 6x +4 as our final answer. I hope you find this video helpful, and be sure to ask any questions down in the comments! Song at the end is one I wrote called "To the Moon and Back". +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic