Brainsteem Mathematics Challenges: Integer Powers Function

in mathematics •  4 months ago

This is a harder version of the puzzle posted here, hence the red icon.


Let x and y be positive integers, such that

f = xy

(or f = x^y if you can't see the superscripts)

and x + y = 80.

Find the highest value of f.

You may leave the answer as a power function ab.

A reminder that these questions should be done without any electronic aid.

There are very few calculus questions, if any, in most mathematics challenges. I assume this is because there are few tricky questions; once you understand the algorithms, differentiating and integrating can be tedious but fairly procedural. This question has a bit of calculus that is often missed out in some courses, but should be interesting to those doing some form of advanced calculus at school.

The last step will have most people reaching for a calculator! However, assuming that it is doable without one, how would you proceed?

The first correct answer and further interesting comments will be rewarded with an upvote. Please show your method, or at least the key steps.


More Brainsteems coming soon...

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a = 0
b = 0

For x = 1 to 79
    y = 80 - x
    f = x^y
    If f > v Then
        v = f
        a = x
        b = y
    End If

WScript.Echo a & "^" & b

prints 20^60

Thanks for witness vote by the way. ^_^


Perhaps I should reboot the computational mathematics challenges I used to post :-)
They were mildly popular compared to the analytical maths puzzles.

BTW like most people, rarely look at my witness votes, but was time for a few tweaks, so you're welcome!

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