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.
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