Econ 221 Chapter 6 appendix supplement -- You will not be tested on this material.Understanding the Slope of a Line at a Point: The Graphical Interpretation of a DerivativeA derivativemeasures the instantaneous rate of changein y when y is some function of x: y = f(x). For a graphical representation of the function y = f(x), the derivative at a specific point is the slope of the function at that point. The slope of a functionis the ratio of change in vertical distance (rise) to the change in horizontal distance (run) as a point moves along the function (line) in either direction. The slope of any straight line is a constant ⇒the rate of change of y as x changes is constant over the length of the line. However, for other, nonlinear curves such as a PPC or indifference curve, the slope is not constant and must be determined for each particular point of interest. Consider a point (x0, y0) on the curve y = f(x), and another point (x1, y1). The slope of the line (called a secant) joining these two points (defined as “m”) is:
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