Maxima minima of function of several variables

Thread starter Neitrino
Start date May 4, 2012
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Function Maxima Minima Variables

In summary, the maxima minima of a function of several variables refer to the points on the function where the rate of change is either maximum or minimum. To find these points, the partial derivatives of the function must be set equal to 0 and solved for the variables. These points can either be local or global maxima/minima. In real-life applications, maxima and minima are used to optimize processes and find efficient solutions in fields such as economics, engineering, and physics.

May 4, 2012

Neitrino

Could you pls advise me any reference (textbook for example) where I can find how to calculate maxima minima of function of several variables... or drop a couple of lines here..

Thank you

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May 4, 2012

micromass

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Check out http://en.wikipedia.org/wiki/Second_partial_derivative_test

Related to Maxima minima of function of several variables

1. What is the definition of maxima minima of a function of several variables?

The maxima minima of a function of several variables refers to the points on the function where the rate of change is either maximum or minimum. These points are also known as critical points.

2. How do you find the maxima minima of a function of several variables?

To find the maxima minima of a function of several variables, you must first take the partial derivatives of the function with respect to each variable. Then, set these partial derivatives equal to 0 and solve for the variables. The resulting values will be the coordinates of the critical points.

3. What is the difference between a local maxima/minima and a global maxima/minima?

A local maxima/minima refers to a point on the function where the rate of change is either the highest or lowest within a specific region. A global maxima/minima, on the other hand, refers to the overall highest or lowest point on the entire function.

4. Can a function have more than one maxima or minima?

Yes, a function of several variables can have multiple maxima and minima. These points can either be local or global maxima/minima.

5. How are maxima and minima used in real-life applications?

Maxima and minima of a function of several variables are used in various fields such as economics, engineering, and physics to optimize processes and find the most efficient solutions. For example, in economics, maxima and minima are used to find the optimal production levels for a company, while in engineering, they are used to design structures with the least amount of stress.