Calculus?
Here’s a problem whose solution was known before 1630. Newton was born in 1642, so his calculus was not used to solve it, but it yields nicely to derivatives. How would you solve it, with or without calculus?
Given a line, divide it into two parts so that the product of the parts will be a maximum.
To see how Fermat solved it, and to see how calculus problems were solved before calculus. look here: https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1984/0025570x.di021131.02p02223.pdf
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