Unit V: BQ#7: Concepts 1-5

How is the difference quotient derived? 

The difference quotient is derived from the slope of a secant line. The difference quotient is of course f of x plus h minus f of x divided by the letter h. We know that the difference quotient is derived from the slope of a secant line because we would have to find the different quotient in order to then find the slope of the secant line. To find the derivative of the difference quotient we do all of this work but with the left over h's we have to plug in zero for them. 

Once we do this then we set our equation equal to zero, eventually finding our slope intercept form.