Difference Quotient

Hello, this is Tom from everystepcalculus.com. I’m gonna do the difference quotient for you today or what others call the definition of a derivative. We’re gonna get started. Turn calculator on, press 2nd Alpha and put index the alpha again, then 8, then () and press enter. Up comes my program menu, you can see the things I’ve programmed so far. There is a graphing section with the calculus and graphing, maximum and mins among others. But today we’ll be doing a definition of a derivative or difference quotient, which ever you know, either one will take you to the program. Press enter and you are in the actual program. Every time you see pause here, you can enter. We’re gonna put in an example, for instance, (you have to press alpha first when you put anything for these boxes) I like to use 7*^2-7*x. Now you’re gonna substitute for every x in the function, x+h Should look like this: f(x) =7*x^2-7*x select ok or change it if you want. This is the formula, the f ‘ of x = the limit as h goes to 0 h represents the change of x. Formula should be: f’ (x) = lim h->0 = f (x+h)- f (x) h h represents x Jot down on your paper then put in your function. Notice I’ve substituted “x+h” for every function and the original function all divided by h. F’ (x) 7*”x+h”^2-7*”x+h” = -(7*x^2-7*x) h Very complicated program, took me a long time, maybe a month to do this program. Worked a lot with research to do it, calculus books and such. So, you’re gonna write this on your paper, but you’ve taken the x squared of the function and worked it out. F’ (x) 7*x^2+14*h*x+7h^2 “-” (7*(x+h)) -(7*x^2-7*x) h Keep writing these down and eventually you’ll get: F’ (x) = lim h->0 =14*x+7*h-7 @ h=0 Answer = 14*x-7 And you’ve gotten a hundred percent on that problem and you look like you know what you’re doing and everything else. Everystepcalculus.com you can go to a new problem, main menu or you can quit or do what you want. Enjoy my programs.