The difference quotient, which is shown in the link below, comes from the slope of the secant line through two points on the graph of f. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative. The difference quotient allows you to find the slope of any curve or line at any single point. The difference quotient is the change in "y" divided by the change in "x." The only difference is that in the slope formula, y is used as the y-axis, but in the difference quotient, the change in the y-axis is described by f(x).
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