Locate and classify all extrema as absolute or relative

[Jacobpm64]

http://img33.imageshack.us/img33/9021/graph3jc.jpg

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)

 

[benorin]

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]

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

 

[Jacobpm64]

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]

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