(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We are given a word problem and asked find maxima/minima (ie a simple example would be to find the least amount surface area required to build a box of a given volume).

Is it necessary to explicitly show that the relative interior max/min, calculated by setting the gradient to 0, is also the absolute extremum by evaluating possible extrema on the boundaries of the domain of the function, even when the physical considerations of the problem render it blatantly obvious that considering the boundaries will not yield a reasonable answer?

For example, for the aforementioned box problem,

x = length of box

y = width of box

z = height of box

The Domain of the box is

D --> { x,y,z : x [tex]\geq0[/tex], y[tex]\geq0[/tex], z[tex]\geq0[/tex] }

Must we explicitly evaluate boundary situations for when x=0 , y=0, z=0 ? (In this case, we see immediately that the volume will be 0) What about for the cases where x is large?

Do I also need to take the limit of x, y, and z to infinity?

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# Homework Help: Boundary considerations in extremum problems

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