Thread: Analysis Function

Is there a function such that, f is continuous on (1,5), reaches a maximum on (1,5), but does not reach a minimum on (1,5). Does such a function exist or is it impossible?

Originally Posted by thahachaina

Is there a function such that, f is continuous on (1,5), reaches a maximum on (1,5), but does not reach a minimum on (1,5). Does such a function exist or is it impossible?

f both reaches a maximum on (1,5) and a minimum on (1,5), never heard of that => i guess it reaches a max on (1,5), but not a minimum on (1,5) is possible.

Originally Posted by thahachaina

Is there a function such that, f is continuous on (1,5), reaches a maximum on (1,5), but does not reach a minimum on (1,5). Does such a function exist or is it impossible?

Hint, basically think of a function that when differentiated gives a function such that

This sounds hard, but it isn't. Think of trigonmetric function with an altered period for one.

Thanks man. I kinda thought about it, but it looks to me like that function is not possible since it does not reach a maximum at (1,5). Is that right?

Originally Posted by thahachaina

Is there a function such that, f is continuous on (1,5), reaches a maximum on (1,5), but does not reach a minimum on (1,5). Does such a function exist or is it impossible?

has a maximum at but has no minimum on the open interval .

(If it were a closed interval it would be a different matter)

CB