Question

find two positive numbers that satisfy the given requirements.

The sum of the first number squared and the second is 27 and the product is a maximum

Answer 1

\[x^2+y=27\]

Answer 2

@agent0smith @Hero @phi

Answer 3

So y = 27 - x^2

set x = 0, to find y

Answer 4

y=27

Answer 5

\[product P=x^2y=x^2(27-x^2)=27x^2-x^4\]
\[find \frac{ dP }{dx } and~ put =0,find ~the~values~of~x\]
then find\[\frac{ d^2P }{dx^2 } at this point\]