extreme value theorem

[Arushi :))]

the sufficient conditions for extreme points say that the fn be continous on a closed & bounded interval [a,b]
for the function y=f(x)
in (a,b) the fn doesnt have extreme point...
but if we consider [a,b] then the end points are d extreme points..????
a- min point and b  the maximum point???

[Akshay Jain]

i think in this case the sufficient condition is dat the function should be continuous and strictly increasing over the intrval [a,b] for a -min annd b - max points......
but m not sure....if sm1 no pls confirm

[Dreyfus]

If minimum occurs at 'a' nd maximum occurs at 'b' then the condition acc to me should be that f(a)<f(x)<f(b) for all xE(a,b) no matter the function decreases or increases in dat open interval.

[economist]

You are confusing extreme points with boundry points. A and b in this example are boundry points and need not be extreme points per se. But if its given that they are extreme points  BUT SILENT ABOUT  WHICH ONE OF THEM IS MIN AND WHICH ONE IS MAX. only thing we can say is function is montonic. NOTE THAT IT CAN BE INCREASING OR DECREASING AND IT NEED NOT BE STRICTLY MONOTONIC. as exreme value theorem doesnt say anything about UNIQUENESS.