Throughout this entire year, we have practiced and memorized the difference quotient through song, and rhythm. In order to understand it, one must know that it is derived from the slope of a secant line, that touches two points on the function.
http://cis.stvincent.edu/carlsond/ma109/DifferenceQuotient_images/IMG0413.JPG
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Secant_line_and_curve_basic.svg/450px-Secant_line_and_curve_basic.svg.png
http://mathinsight.org/media/image/image/neuron_firing_rate_kink_tangent_line.png
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