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

On Sat, 3 May 2025 19:01:15 +0000, Richard Tobin wrote:

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!!!
>
_______________
>
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

______________________________________
Thank you...      When i saw that this curve looks like the typical
curve
for
    y= x^3 + bx^2 + cx + d
it made more sense that this "car"  starts (at x=0) at the Top speed (of
1)
       but gradually slows down to a halt  (at x=1/2)
What's not at all obvious (intuitive) for me is.... why or how
                       the max Volume is achieved at   x=1/6
                     Could  a  little  child  guess that correctly ?