The sum is s and the product is a maximum


Asked by wiki @ in Mathematics viewed by 40 People


Find two positive real numbers whose product is a maximum. the sum is 80

Answered by wiki @



Let's say the numbers are "a" and "b"

thus \bf y=ab\qquad 
\begin{cases}
a+b=80\\
b=80-a
\end{cases}\implies y=a(80-a)\implies y=80a-a^2\\\\
-----------------------------\\\\
\cfrac{dy}{da}=80-2a

set the derivative to 0, and check the critical points, there's only one anyway

and do a first-derivative test, to see if it's a maximum

Do you know the better answer?

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