# How to Find the Absolute Extrema of a Function Over a Defined Region?

• MHB
• harpazo
In summary: My apologies. In summary, the task is to find the absolute extrema of the function f(x,y) = 12-3x-2y over the triangular region R in the xy-plane with vertices (2,0), (0,1), and (1,2). This can be done by following the method outlined by HallsofIvy in the previous post, which involves finding the critical points of the function within the region and evaluating the function at these points as well as at the vertices of the region. The maximum and minimum values obtained will be the absolute extrema for the function over the given region.
harpazo
Find the absolute extrema of the function over the region R. (In this case, R contains the boundaries.)

f (x, y) = 12 - 3x - 2y

R: The triangular region in the xy-plane with vertices (2, 0), (0, 1), and (1, 2).

I need the steps to guide me through this monster question. I am familiar with relative extrema but so much absolute extrema questions.

Hmm...you posted the same question before and HallsofIvy provided a very thorough method for determining the absolute extrema here:

http://mathhelpboards.com/calculus-10/find-absolute-extrema-over-region-r-20883-post94881.html#post94881

I know you are new here, and I'm only pointing out one of our policies as is my duty, but in the future, please don't post the same question more than once, as it can lead to duplication on the part of our helpers, whose time is valuable.

Is there some reason you found the help previously provided to be insufficient? If this is ever the case, please feel free to reply in the same thread to say what about the given help you don't understand. :D

MarkFL said:
Hmm...you posted the same question before and HallsofIvy provided a very thorough method for determining the absolute extrema here:

http://mathhelpboards.com/calculus-10/find-absolute-extrema-over-region-r-20883-post94881.html#post94881

I know you are new here, and I'm only pointing out one of our policies as is my duty, but in the future, please don't post the same question more than once, as it can lead to duplication on the part of our helpers, whose time is valuable.

Is there some reason you found the help previously provided to be insufficient? If this is ever the case, please feel free to reply in the same thread to say what about the given help you don't understand. :D

I forgot that a similar question has already been posted.

## 1. What is an absolute extrema?

An absolute extrema is a value that represents the highest or lowest point of a function over a given interval. It can also be referred to as the global maximum or minimum.

## 2. How is an absolute extrema different from a relative extrema?

A relative extrema is a value that represents a local maximum or minimum within a specific interval, while an absolute extrema is the highest or lowest point of the entire function over a given interval.

## 3. How do you find the absolute extrema of a function?

To find the absolute extrema of a function, you must first take the derivative of the function and set it equal to zero to find the critical points. Then, evaluate the function at each critical point and the endpoints of the interval to determine the absolute extrema.

## 4. Can a function have more than one absolute extrema?

Yes, a function can have multiple absolute extrema if the function is not continuous or if the interval is not closed.

## 5. How are absolute extrema used in real-world applications?

Absolute extrema are used in many real-world applications, such as finding the maximum or minimum value of a stock over a certain period of time, determining the ideal temperature for a chemical reaction, or finding the maximum or minimum production rate for a manufacturing process.

• Calculus
Replies
3
Views
4K
• Calculus
Replies
5
Views
1K
• Calculus
Replies
4
Views
2K
• Calculus
Replies
1
Views
2K
• Calculus
Replies
20
Views
2K
• Calculus and Beyond Homework Help
Replies
11
Views
2K
• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus
Replies
1
Views
2K
• Calculus and Beyond Homework Help
Replies
7
Views
3K
• Calculus and Beyond Homework Help
Replies
6
Views
2K