Two variable extreme value problem

In summary, to solve an extreme value problem, one must use f base xy, which is the original function differentiated with respect to both x and y while keeping the other variable constant. This concept may have been missed in class.
  • #1
KaiserBrandon
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Homework Statement


alright so this is just a general question. In order to solve an extreme value problem, there's a part where I have to use f base xy. I'm not quite sure what that is, I know f base x is the partial derivative of the function with regards to x, and f base xx is the second partial derivative for x.


Homework Equations



none

The Attempt at a Solution


The only thing I can think of is that f base xy is simply the original function of x and y. Thanks in advance
 
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  • #2
F base xy means differentiate with x while keeping y constant, then take the rest and differentiate with respect to y keeping x constant.
example:
f(x,y)= 3x^2+2xy
f(x,y)x = 6x+2y
f(x,y)xy = 2
 
  • #3
ok you that makes sense. I guess I must have missed the class where we learned that lol. Thanks.
 

FAQ: Two variable extreme value problem

What is a two variable extreme value problem?

A two variable extreme value problem is a type of optimization problem that involves finding the maximum or minimum value of a function with two independent variables, subject to certain constraints. This type of problem arises in various fields, such as economics, engineering, and physics.

How do you solve a two variable extreme value problem?

To solve a two variable extreme value problem, you can use a variety of methods, such as the method of Lagrange multipliers, the method of substitution, or the method of partial derivatives. These methods involve finding critical points and using them to determine the maximum or minimum value of the function.

What are the applications of two variable extreme value problems?

Two variable extreme value problems have many real-world applications, including finding the optimal production levels in a manufacturing plant, determining the best investment portfolio, and maximizing profits in a business. They are also used in fields such as meteorology, genetics, and statistics.

Can two variable extreme value problems have more than one solution?

Yes, it is possible for a two variable extreme value problem to have multiple solutions. In some cases, there may be more than one local maximum or minimum, or the function may have a saddle point. It is important to carefully analyze the problem and consider all possible solutions.

Are there any limitations to solving two variable extreme value problems?

One limitation of solving two variable extreme value problems is that they can become very complex and difficult to solve when the function has multiple variables and constraints. In some cases, it may not be possible to find an analytical solution, and numerical methods may need to be used instead. Additionally, the solutions obtained may not always be feasible in practical applications.

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