Difference Quotient
The difference quotient is a formula that finds the slope of the secant line and will help us find the slope of any given slope of a tangent line. Since the difference quotient is used for the slope, it is derived from the slope formula.
Using the slope formula of y2-y1/x2-x1, we know that the x1 and y1 is just x because that is our first point on the graph.The second point is unknown so it is x + the change in height which is h, (x+h). We now plug in the (x+h) for x2 and y2. This gives us (x+h)-y1/(x+h)-x1. In the denominator we have the x's canceling and that would leave us with (x+h)-y/h. Or (x+h)-x/h. This is how we derive the difference quotient from the slope formula.
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