Re: Maximize Cistern Volume -- (cut out 4 squares (at Corners) and discard them)

In article <016b2820b7160c571e97a7f320260176@www.novabbs.com>,
HenHanna  <HenHanna@dev.null> wrote:

I let the derivative be 0 and solve it ,  and i get     x = 1/2,   1/6
>
           at  x=0  the slope is 1
  whereas  at  x=1/2,  the slope is Zero!!!
>
_______________
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at  x=1/2,  the slope is Zero!!!
>
        It's not obvious why,   Can someone explain this?

When x is 1/2 the side of the cistern has shrunk to zero, the height
is 1/2, and the volume is zero.  Physically, x can't exceed 1/2, but
the formula just produces a negative length for the side of the
cistern (along with a height greater then 1/2).  That gives a positive
volume (the negative length is squared), so x=1/2 is a minimum for the
volume.

-- Richard