BQ. #7 Unit V

Where does the difference quotient come from?? (f(x+h)-f(x))/h


This graph will help to get a visual on what we are talking about. A secant line is present in this graph. (Secant line- a line that touches the function at two points.) The very first point is know as (x,f(x)) and the second point as (x-h, f(x-h)) since it has an h difference from the first one. (As seen on this graph.)

 You then plug this into the slope formula, m=(y1-y2)/(x2-x). The x's will cancel in the denominator and just leave h on bottom. For the numerator we just leave it as it is because sometimes x is squared so we must use (x+h)^2, The final equation should be (f(x+h)-f(x))/h

The top picture can be found here.