The difference quotient is the slope of a secant line through two points of a curve.
In the difference equation, h is the change in x and f(x+h)-f(x) is the change in f(x) given the change in h.
The difference quotient is used in calculus. As the two points grow closer together, the closer the slope of the secant line is to the slope of the curve. This gives the expression at the base of calculus:
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