Asked by Andrea

Hello, I'm supposed to do this questions using concepts of differentiation with proper workings, and not based on general knowledge.

Question: If x + y = 82, find the maximum value of xy.

I know that 41 and 41 would give the greatest product... but how should i work it out with workings??
Answered by drwls
Express the product P as a function of one variable, and set the derivative with respect to that variable equal to zero.

y = 82 - x
Product: P = x y = 82x - x^2
dP/dy = 82 - 2x = 0
x = 41
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