# Locate and classify all extrema as absolute or relative

http://img33.imageshack.us/img33/9021/graph3jc.jpg [Broken]

Ok, I had a function and the directions were:

Locate and classify all extrema as absolute or relative...

I can't remember the equation, but when i found the critical numbers of the function.. i got a critical number at the origin.. but when i graphed it on the calculator.. i got the graph above.. what is (0,0).. Is it anything? I don't think it's a max or min at all.. why would i get a crit # but no max or min.. just at an odd place like that... where the graph begins... To me, the answer would only be.. an absolute minimum at around (2, -2) or whatever it is (i didn't label the axes.. but you understand what i mean)

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benorin
Homework Helper
Critical numbers are not always extrema, they also indicate where the derivative does not exist, saddle points (and what else I can't think of...)

HallsofIvy
Homework Helper
Do know what "extrema" MEANS?? If so solving this is just a matter of looking at the graph!

extrema points where it's either higher than all points around.. or lower than all points around...

so would (0,0) be a relative max?..

my confusion is.. does it have to have a hill or a valley (does it have to go up then come back down.. or go down and come back up)... because at (0,0) it is just one side of the hill..

benorin
Homework Helper
Yes, (0,0) is a relative max, that is: there is some interval about 0 in which f(x) < f(0).