BQ#7- Unit V

Where does the formula for the difference quotient comes from?

The difference quotient formula comes from the secant line that touches the graph twice meaning there's two points. The first point is ( x , f(x)) and the second point is (x+h , f(x+h)), from there we find the slope of the secant line which is y2-y1/x2-x1. We substitute the y and x with the given points from the secant line and will turn out to be f(x+h) - f(x)/x + h -x. Then we see that there are variables that cancel each other -x and +x from the denominator then just leaving "h". That's how you get the difference quotient formula f(x+h) - f(x)/h.