2.6: Multivariable Extrema

Math 4A: Multivariable Calculus · LibreTexts

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Learning Objectives
    • Use partial derivatives to locate critical points for a function of two variables.
    • Apply a second derivative test to identify a critical point as a local maximum, local minimum, or saddle point for a function of two variables.
    • Examine critical points and boundary points to find absolute maximum and minimum values for a function of two variables.
    • Use the method of Lagrange multipliers to solve optimization problems with one constraint.
    • Use the method of Lagrange multipliers to solve optimization problems with two constraints.

    One of the most useful applications for derivatives of a function of one variable is the determination of maximum and/or minimum values. This application is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.

     

    This page titled 2.6: Multivariable Extrema was last modified on Wed, 20 Aug 2025 01:15:11 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Kenn Huber.