# end-point extrema

• Oct 7th 2011, 01:22 AM
Stuck Man
end-point extrema
Is this book wrong about point B? I think it is an end-point but not an end-point minimum. The function at 0 has a lower value.
• Oct 7th 2011, 02:03 AM
magicka
Re: end-point extrema
Book is correct here:
And end-point minimum if there exists a region in the domain for which B is an end-point (you agreed it's true) and for which $\displaystyle f(B)\leq x, \forall x$. Note: if exists a region, so it doesn't have to be for every region (that would be definition of minimum), but only for a region (in this example use $\displaystyle [3,4]$)
• Oct 7th 2011, 04:11 AM
Stuck Man
Re: end-point extrema
Thanks. I had started to think it is correct. Surely you are talking about B not A?
• Oct 7th 2011, 04:19 AM
magicka
Re: end-point extrema
yes, my mistake, I've edited previous post!
• Oct 7th 2011, 05:50 AM
Stuck Man
Re: end-point extrema
In this example C and D are end-point minimums aren't they?
• Oct 7th 2011, 07:12 AM
magicka
Re: end-point extrema
Nope; even though they satisfy second condition they are not endpoints!
• Oct 7th 2011, 07:44 AM
Stuck Man
Re: end-point extrema
They are end-points of the second and third functions. The book definitely describes these as end-points.
• Oct 7th 2011, 07:55 AM
magicka
Re: end-point extrema
Could you please copy here how end-point is exactly defined?

And you are watching endpoints of $\displaystyle f(x)$, not every part of it. By that logic you could split function above (one that is defined on -2 to 4) split into infinite many parts and have infinite many end-points.
• Oct 7th 2011, 08:07 AM
Stuck Man
Re: end-point extrema
Unfortunately it is not defined.
• Oct 7th 2011, 08:10 AM
Stuck Man
Re: end-point extrema
The book does talk about C and D as being at end-points of the subdomains.
• Oct 7th 2011, 08:35 AM
Stuck Man
Re: end-point extrema