optimisation

[Sarahisme]

hey all, my textbook has this sample question...

 

"Find the shape of a reectangular box with no top having given volume V and the least possible total surface area of its five faces."

 

now the book has the soluition, i.e. you just do

 

S = xy + 2yz + 2xz

 

and

 

V = xyz

 

and you end up finding just one critical point.

 

my question is why should this point be a minimum?

 

-sarah

[BobbyJoeCool]

SA should be a minimum (given your equation). because you're trying for the smallest possible SA. So you can proceed to find the min point(s) of your equation.

[Ducky Havok]

Also, you could probably do a sign test around the point. If it's a minimum, it'll be negative to the left of the point and positive to the right, and if it's a maximum it'll be positive then negative.

[Sarahisme]

i tryed doing the sign test, but it didnt work, so yeah. .... i dunno what to do