Find the max volume of a box with a square base if you have 1200 sq. ft. of material for sides and a bottom (assuming open top).
I'm screwing up somewhere but I can't figure out where. V= x^2*y and then your y= (1200-x^2)/4x
Using a graphical method I found the answer x to be 20. But how do you get here using calculus?
Okay, I see that you substituted the y equation immediately into the volume equation.
Why couldn't you take the derivative of x^2*y to get:
vol'(x)= x^2((1200-x^2)(4) - 4x(-2x))/(4x)^2 + 2xy
as in lets v=X^2 and let u=y
then vol'(x)= v*u' + u*v'
When I work this out I get x=60 and y= -10 which is obviously NOT the answer