- #1
Andrax
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find the max value of xy (done in a "weird" way)
so our teacher assigned this homework in the last 10 minutes
we haven't read the function with 2 variables and I've never seen/used one
(things were just getting in my head since it's only 10 mins i don't know if I'm making a mistake)
suppose that x and y satisfie 4x+y=2
find the maximum value of xy
so this is done with deriviatives but i was thinking in using another way and it turned to be right , what I'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how I've done it
f(x)=4x+y-2 must be eqUAL TO 0
f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
anyway this leads to x=2-y/4y
replacing in 4x+y=2 we get y= 1 then x=1/4
now our teacher used derviatives to solve this
y=2-4x
xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
thanks everyone :)
Homework Statement
so our teacher assigned this homework in the last 10 minutes
we haven't read the function with 2 variables and I've never seen/used one
(things were just getting in my head since it's only 10 mins i don't know if I'm making a mistake)
suppose that x and y satisfie 4x+y=2
find the maximum value of xy
so this is done with deriviatives but i was thinking in using another way and it turned to be right , what I'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how I've done it
f(x)=4x+y-2 must be eqUAL TO 0
f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
anyway this leads to x=2-y/4y
replacing in 4x+y=2 we get y= 1 then x=1/4
now our teacher used derviatives to solve this
y=2-4x
xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
thanks everyone :)
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