The difference quotient is derived by using the slope formula: (y2-y1/x2-x1). Looking at the video above, from the graph that he drew, the first point is called "x1" and the "h" is the distance from one point to the other. That point would then be "x+h" ( this would be x2). The y values arefound by looking at the function, f(x). We plug in the x1 value "x" and we would get f(x). For our x2, we plug in "x+h" into our function and we would get f(x+h).
y2= f(x+h)
y1= f(x)
x2= "x+h"
x1= "x"
From there, we simply plug in those into the slope formula.
We would get f(x+h) - f(x) over x+h-x. The x's on the bottom would cancel each other out. And we are left with f(x+h)-f(x)/h which is the difference quotient.
