anonymous
  • anonymous
Math help!
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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ybarrap
  • ybarrap
This is concave up |dw:1436133062471:dw| Can guess what it looks like for concave down? That's why f''(x) tells you if an extrema is a max or a min. If f'(x) < 0 then f'(x)=0 is min, if f''(x> > 0 then f'(x)=0 is a max
ybarrap
  • ybarrap
|dw:1436133272968:dw|
anonymous
  • anonymous
So we see that C is false.

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ybarrap
  • ybarrap
You are correct. f''(x) < 0 means concave DOWN |dw:1436133399021:dw| Here is how to remember what sign of f''(x) means: |dw:1436133435469:dw|
ybarrap
  • ybarrap
*I meant f''(x)
ybarrap
  • ybarrap
|dw:1436133535569:dw|
ybarrap
  • ybarrap
Mouth says min or max
anonymous
  • anonymous
So would it be D?
ybarrap
  • ybarrap
|dw:1436133612871:dw|
ybarrap
  • ybarrap
You know why B is false, right? https://en.wikipedia.org/wiki/Inflection_point#A_necessary_but_not_sufficient_condition
anonymous
  • anonymous
Not really
ybarrap
  • ybarrap
Just because f''(x)=0 doesn't mean that that point is an inflection point. However, if that point is an inflection point then f''(x)=0. I hope this distinction makes sense. This is like saying if A is true then B is true. However, this does not mean the same as if B is true then A is true. Same logic. For A: If a function is defined in a closed interval, then there are real numbers defined at every point in that interval. If you have any set of real numbers, you can always find the maximum and minimum of this set. Do you agree?
anonymous
  • anonymous
Yes I do
ybarrap
  • ybarrap
Good!
ybarrap
  • ybarrap
"A" does NOT mean that the Global min and max are in this interval it just means that there IS a max and min in that interval.
anonymous
  • anonymous
So its wrong?
ybarrap
  • ybarrap
No, it's right. Just want to make the distinction between a Global and Local (absolute) min and max.
anonymous
  • anonymous
Okay thank you so much! You're very helpful!
ybarrap
  • ybarrap
You're welcome!

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