Unit V Biq Questions

Explain in detail where the formula for the difference quotient comes from now that you know!  Include all appropriate terminology (secant line, tangent line, h/delta x, etc). 

A  represents the tangent line. B represents the secant line.


The difference quotient is the rate of change of a secant line. The formula for finding the difference quotient is: y2-y1/x2-x1.  A secant line touches the graph twice.
Difference Quotient:

We can find the derivative by using the difference quotient.
Initially, the derivative is when we evaluate the limit (lim -> 0) of the difference quotient. It helps us find the slope of the tangent line (touches the graph once) in a graph. We do this because the smaller the delta x (h/change) is, the more the secant and tangent line resemble each other. We use lim -> 0 in order to make the delta x as small possible (a function can have diff. derivatives at the value of x). :)

Work Cited:
Graph: http://www.analyzemath.com/calculus/Differentiation/difference_quotient.html
Diff. Quotient image: http://www.coastal.edu/mathcenter/HelpPages/Difference%20Quotient/img001.GIF