1. ## 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.

2. ## 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 $f(B)\leq x, \forall x$. 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 $[3,4]$)

3. ## Re: end-point extrema

Thanks. I had started to think it is correct. Surely you are talking about B not A?

4. ## Re: end-point extrema

yes, my mistake, I've edited previous post!

5. ## Re: end-point extrema

In this example C and D are end-point minimums aren't they?

6. ## Re: end-point extrema

Nope; even though they satisfy second condition they are not endpoints!

7. ## Re: end-point extrema

They are end-points of the second and third functions. The book definitely describes these as end-points.

8. ## Re: end-point extrema

Could you please copy here how end-point is exactly defined?

And you are watching endpoints of $f(x)$, 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.

9. ## Re: end-point extrema

Unfortunately it is not defined.

10. ## Re: end-point extrema

The book does talk about C and D as being at end-points of the subdomains.