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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 tex2html_wrap_inline440 is small.



Let tex2html_wrap_inline450 denote the demand for gas at price x. The rate of change is given by the derivative


Since tex2html_wrap_inline456 , 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.


Michael A. Trick
Mon Aug 24 13:43:30 EDT 1998