Extremum values of function of two variable....[
Автор: 𝐋𝐎𝐆𝐈𝐂 𝐋𝐀𝐍𝐄
Загружено: 2023-02-23
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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.
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.
Critical Points
For functions of a single variable, we defined critical points as the values of the variable at which the function's derivative equals zero or does not exist. For functions of two or more variables, the concept is essentially the same, except for the fact that we are now working with partial derivatives.
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