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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
So we see that C is false.
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|
*I meant f''(x)
Mouth says min or max
So would it be D?
You know why B is false, right? https://en.wikipedia.org/wiki/Inflection_point#A_necessary_but_not_sufficient_condition
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?
Yes I do
"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.
So its wrong?
No, it's right. Just want to make the distinction between a Global and Local (absolute) min and max.
Okay thank you so much! You're very helpful!