BQ#7

you know there is a tangent line on the graph when the line only touches the graph once as you can see in the picture

on thispicture the line touches the graph twice which meants it is a secant line. this changes which the coordinates are (x+h, f(x+h) )

with this we can derive the quotient formula and by that we plug in the secant coordinates to our slope formula which is y2-y1/x2-x1 when we plug everything in all we need to do is cancel the x's and end up with the formula which is  (f(x+h)-f(x)) /h