Path: ...!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail
From: HenHanna <HenHanna@dev.null>
Newsgroups: rec.puzzles,sci.lang,sci.math
Subject: Re: Maximize Cistern Volume  -- (cut out 4 squares (at Corners) and discard
 them)
Date: Tue, 6 May 2025 19:35:47 +0000
Organization: novaBBS
Message-ID: <14b4afbbf6091c2c839beec0c3c41f21@www.novabbs.com>
References: <016b2820b7160c571e97a7f320260176@www.novabbs.com> <vv5p5r$2lbu9$1@artemis.inf.ed.ac.uk>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: i2pn2.org;
	logging-data="3419509"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="4L8HabKtc1alsSAOmk7EUGDHKRhgGhC+6gJMfTsJB0A";
User-Agent: Rocksolid Light
X-Rslight-Posting-User: abae1fed5a82111a8790dc84735f550edb4392db
X-Rslight-Site: $2y$10$FWMmrqMUcfBfxJ2s9xyxNuDPdzfOgN0hLczqaynLxUGjnNEYxFDnq
X-Face: P#KeQ)CUdd!==@fw~Ms1=,Hb`IWtb6:Mw)x3B=H1BfNC\lz?Nb&)M9}$>?'X7l;CuB}utlJ=PHsRBSG6X>dYZ$[>P]$~+`>@V6$t}hTLoQ7XC~W\>:`B3ALU]SH;d(\MEc}znW8m}-ma&yPFkJ2@KSQrz=!Y;><;6a>z6N+mt`ClCt.PAE<o+B$qjwejZSZ,w]^;vrdl24z5(pm={l,F10qRDF
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 2600
Lines: 40

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 ?