Question

what is the maximum value of xy when x+y =3

Answer 1

xy=x(3-x)=3x-x^2
differentiating this will give
3-2x
in maximum differentiation is zero
3-2x=0
x=1/2

Answer 2

and answer is ?

Answer 3

you know x,
substitute it to x+y=3 and find y
and then multiply x and y

Answer 4

thanks

Answer 5

(y)

Answer 6

that idea word, except for the last step
3-2x=0

you get 3= 2x and x= 3/2 (not ½)

Answer 7

yes. sorry, my bad

Answer 8

Mathematica confirms phi's answer.
Refer to the attachment where Maximize is a function from Mathematica's Constrainted Optimization function suite.