Sarahisme Posted October 15, 2005 Share Posted October 15, 2005 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 Link to comment Share on other sites More sharing options...
BobbyJoeCool Posted October 15, 2005 Share Posted October 15, 2005 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. Link to comment Share on other sites More sharing options...
Ducky Havok Posted October 15, 2005 Share Posted October 15, 2005 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. Link to comment Share on other sites More sharing options...
Sarahisme Posted October 16, 2005 Author Share Posted October 16, 2005 i tryed doing the sign test, but it didnt work, so yeah. .... i dunno what to do Link to comment Share on other sites More sharing options...
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