Unit V Big Question

Where does the formula for the difference quotient come from?

The difference quotient formula is:
f(x + h) - f(x) / h

H is also known as delta x.

In a graph, one can find a secant of the graph by using two points and finding the slope of this secant. One point would be (x, f(x)). The second x-value would be delta x units away which would make the second point (x + delta x, f(x + delta x)). Using the slope formula: y2 - y1 / x2 - x1 we would get the difference quotient if you substitute delta x for h and if you combine like terms correctly you would get the difference quotient formula above. However, one would only get the slope of a secant formula but to ensure one gets the slope of the tangent line, one must place a limit and more specifically a limit that has h approaching 0.