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 Derivative
A
derivative
measures the instantaneous rate of change
in 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 function
is 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 (x
0
, y
0
) on the curve y = f(x), and another point (x
1
, y
1
).
The slope of the line (called a secant
) joining these two points (defined as “m”) is:
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 Fall '07
 Wadman
 Microeconomics, Derivative, Slope

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