Square root of 4×-1=5
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The area of the box is
which we want to minimize subject to the constraint .
The Lagrangian is
with critical points where the partial derivatives are 0:
Notice that
Substituting the latter into either or
will end up suggesting that
is infinite, so we throw out this case.
If , then
We ignore the case where because that would make the volume 0. Then
so we have one critical point at
which give a minimum area of about 1829.41 sq. cm.