It is important to know the following differentiation formulas:

For a function *f* of one variable *x*, recall that the derivative
*f*'(*x*) is equal to the slope of a tangent line at point *x*.
So, if the function has a positive derivative at point *x*, then
the function is increasing, and if it has a negative derivative,
it is decreasing.
Since the function and its tangent line are close around point *x*,
the following formula can be used when is small.

Let denote the demand for gas at price *x*.
The rate of change is given by the derivative

Since , we get

So demand drops by 2%. The factor relating change in demand to
change in price is known as ``price elasticity
of demand'' in economics (You will learn more about this in 45-749
Managerial Economics and in marketing courses such as 45-720 Marketing
Management and 45-834 Pricing).
Here *f*'(*x*) = -0.2 *f*(*x*), so price elasticity
of demand is -0.2.

Mon Aug 24 13:43:30 EDT 1998