# Maple - Finding maximum of maximums in different functions

• Rafael de Gomes
In summary, the conversation is about finding the highest maximum value out of 11 equations with defined minimum and maximum values. The person is looking for a way to identify which equation has the highest maximum value without writing multiple lines of code. They suggest creating an array of functions and using a loop to determine the maximum value for each function, then searching the array for the maximum value and using the index to retrieve the corresponding function. They also mention that they may not be using the correct terminology for Maple.
Rafael de Gomes
Hello,

I've been trying to come up with a short way of writing the code. What I'm trying to do is:

I have 11 equations, each of which have a defined minimum and maximum. I'm trying to find the highest maximum out of all of them and I need to know which one it is. The highest as in farthest away from zero, so negative values are also required.

I was trying this:

And although this would work (it does give me a value), it doesn't tell me which of the functions is the highest. Is there any way to do this other than wasting a bunch of lines writing:

?

You'll probably want to write a function as far as I can tell. (It's been a while since I used maple so maybe a built-in function exists although highly unlikely)

In essence it would do something like create an array of functions.
Then loop over this array determining the maximum/whatever you need of said function and assign to a new array at the same index (<- this is important)
Then you can determine the maximum of this newly created list
Now the result, you search in your array of maxima and use the index to retrieve your function.

disclaimer: I'm probably using some bad terminology here like the array. An array can be a list or vector or ... in Maple, if I'm not mistaken

## 1. How can I use Maple to find the maximum value of a specific function?

To find the maximum value of a function in Maple, you can use the built-in function "maximize" which takes in the function and the variable of interest as arguments. This will return the maximum value and the corresponding input that gives that maximum value.

## 2. Can Maple find the maximum of a function with multiple variables?

Yes, Maple can find the maximum of a function with multiple variables. You can use the "maximize" function and specify all the variables as arguments. However, the function must be continuous and differentiable for this method to work.

## 3. Is there a way to find the maximum of multiple functions at once in Maple?

Yes, you can use the "maximize" function with a list of functions as the first argument. This will return the maximum value and the corresponding input for each of the functions in the list.

## 4. Can I specify constraints when finding the maximum value in Maple?

Yes, you can use the "maximize" function with an additional argument for constraints. These constraints can be inequalities or equations that the input must satisfy in order to be considered for the maximum value.

## 5. Are there any other functions in Maple that can help me find the maximum value of a function?

Yes, apart from the "maximize" function, Maple also has the "Optimization" package which contains several other functions for finding maximum and minimum values. Some examples include "fsolve", "optimize", and "NLPSolve". These functions may have different syntax and capabilities, so it is important to read the documentation carefully.

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