# Question about max of functions

• alomari2010
In summary, the conversation is about finding the maximum value for a given set of variables, using the formula for max{x,y}. The question is then posed about finding the formula for max{x_1, x_2,..., x_n} for a general set of variables.
alomari2010
Let a,b,c,d in R. For a=< x =< b and c=< y =< d, find

maxx{maxy{(x-a)(y-c), (x-a)(d-y), (b-x)(y-c), (b-x)(d-y)}}??

it is well known that

max(x,y) = $$\frac{x+y+|x-y|}{2}$$

alomari2010 said:
Let a,b,c,d in R. For a=< x =< b and c=< y =< d, find

maxx{maxy{(x-a)(y-c), (x-a)(d-y), (b-x)(y-c), (b-x)(d-y)}}??

it is well known that

max(x,y) = $$\frac{x+y+|x-y|}{2}$$

With x fixed the functions you have are just straight lines... very easy to find max and min!

maxx{maxy{(x-a)(y-c), (x-a)(d-y), (b-x)(y-c), (b-x)(d-y)}}=
maxx{(x-a)(d-c), (x-a)(d-c), (b-x)(d-c), (b-x)(d-c)}=
max{(b-a)(d-c), (b-a)(d-c), (b-a)(d-c), (b-a)(d-c)}==(b-a)(d-c)

Thanks!

but i think you didn't got what i want!

i will try to repost my Q?

As above we have a formula for max{x,y}. So what is the formula for max{x,y,z}?
where x,y,z in R. In general, for x_i in R, i=1,2,..,n
what is the formula for max{x_1, x_2,..., x_n}?

hope anyone can got the answer!

## 1. What is the purpose of finding the maximum of a function?

The maximum of a function is the highest point on the graph and can provide important information about the behavior of the function. It can help determine the most efficient solution to a problem or identify the optimal value for a given variable.

## 2. How do you find the maximum of a function algebraically?

To find the maximum of a function algebraically, you can take the derivative of the function and set it equal to 0. Then, solve for the variable to find the critical points. The largest critical point will be the maximum of the function.

## 3. Can a function have more than one maximum?

Yes, a function can have multiple local maximums. These are points where the function is at its highest value within a specific interval. However, there can only be one absolute maximum, which is the highest point on the entire graph.

## 4. How does finding the maximum of a function relate to optimization problems?

Finding the maximum of a function is essential in optimization problems because it helps identify the most efficient solution. By finding the maximum of a function, you can determine the optimal value for a given variable, which can save time, resources, and effort.

## 5. Are there specific techniques for finding the maximum of a function?

Yes, there are various techniques for finding the maximum of a function, including the first and second derivative tests, the method of Lagrange multipliers, and using graphical methods. The most appropriate technique will depend on the complexity of the function and the available resources.

Replies
3
Views
2K
Replies
2
Views
1K
Replies
11
Views
1K
Replies
9
Views
479
Replies
6
Views
1K
Replies
5
Views
1K
Replies
2
Views
2K
Replies
2
Views
1K
Replies
21
Views
494
Replies
17
Views
2K