MATH 123 Chapter Notes - Chapter 17: Paraboloid, Multivariable Calculus, Production Function

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 123
• Professor: Sidney Trudeau

Document Summary

It is possible to produce three-dimensional graphs of functions of two variables and that the process is greatly enhanced using level curves. Level curves are formed by determining the values of x and y that produce a particular functional value. Level curves are also important in economics and are used to indicate combinations of the values of (cid:1876) and (cid:1877) that produce the same value of production (cid:1878). This procedure was used to analyze the cobb-douglas production function, which has the general form: (cid:1878)=(cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:1876)(cid:1877)1 . Partial derivatives are the extension of the concept of differentiation with respect to one of the variables while the other variables are held constant. Partial derivatives were used to identify extrema of a function of several variables. In particular, we identified all points where the partial with respect to (cid:1876) and the partial with respect to (cid:1877) are both zero, which we called critical points.