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Difference Quotient and Average Rate of Change

The expression (f(x+h) - f(x))/h as the average rate of change of a function over an interval, and its reading as the slope of the secant line through two points on the graph. Includes forming and algebraically simplifying the quotient for polynomial, rational, and radical functions before any limit is taken.

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The Difference Quotient in Calculus

The difference quotient, defined as [f(x+h) − f(x)] / h for a function f, measures the average rate of change of f over an interval of length h and serves as the algebraic precursor to the derivative…