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?
It's sort of like soup cans vis-a-vis fish tins, or the idea
that cans, to get the most volume of a cylinder, have
at least two solutions.
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
What's not at all obvious (intuitive) for me is.... why or how
the max Volume is achieved at x=1/6
In article <14b4afbbf6091c2c839beec0c3c41f21@www.novabbs.com>,
HenHanna <HenHanna@dev.null> wrote:
What's not at all obvious (intuitive) for me is.... why or how
the max Volume is achieved at x=1/6
Note that x=1/6 makes the total area of the sides equal to the area of
the base (4/9). I wouldn't be surprised if that is a special case of
some more general result.
-- Richard
Sysop: | Keyop |
---|---|
Location: | Huddersfield, West Yorkshire, UK |
Users: | 491 |
Nodes: | 16 (2 / 14) |
Uptime: | 107:13:20 |
Calls: | 9,684 |
Calls today: | 5 |
Files: | 13,725 |
Messages: | 6,175,496 |
Posted today: | 1 |