determine from the given graph whether the function has any absolute extreme values on (a, b). then explain…

determine from the given graph whether the function has any absolute extreme values on (a, b). then explain how your answer is consistent with the extreme value theorem.\nc. the function has an absolute minimum value at ( x = b ) but does not have an absolute maximum value on ( (a, b) )\nd. the function does not have any absolute extreme values on ( (a, b) ).\nexplain the results in terms of the extreme value theorem.\na. since the function ( f ) is continuous on a closed interval, ( f ) attains both an absolute maximum value and an absolute minimum value on its domain\nb. since the function ( f ) is continuous and the domain of ( f ) is not a closed interval, ( f ) may or may not have any absolute extreme values on its domain\nc. since the function ( f ) is not continuous and the domain of ( f ) is a closed interval, ( f ) may or may not have any absolute extreme values on its domain\nd. since the function ( f ) is not continuous and the domain of ( f ) is not a closed interval, ( f ) may or may not attain any absolute extreme values on its domain

determine from the given graph whether the function has any absolute extreme values on (a, b). then explain how your answer is consistent with the extreme value theorem.\nc. the function has an absolute minimum value at ( x = b ) but does not have an absolute maximum value on ( (a, b) )\nd. the function does not have any absolute extreme values on ( (a, b) ).\nexplain the results in terms of the extreme value theorem.\na. since the function ( f ) is continuous on a closed interval, ( f ) attains both an absolute maximum value and an absolute minimum value on its domain\nb. since the function ( f ) is continuous and the domain of ( f ) is not a closed interval, ( f ) may or may not have any absolute extreme values on its domain\nc. since the function ( f ) is not continuous and the domain of ( f ) is a closed interval, ( f ) may or may not have any absolute extreme values on its domain\nd. since the function ( f ) is not continuous and the domain of ( f ) is not a closed interval, ( f ) may or may not attain any absolute extreme values on its domain

Answer

Explanation:

Step1: Analyze the function's domain

The domain ((a,b)) is an open interval (not closed as it doesn't include (a) and (b)).

Step2: Recall the Extreme Value Theorem

The Extreme Value Theorem states that if a function (y = f(x)) is continuous on a closed interval ([m,n]), then (f(x)) has both an absolute maximum and an absolute minimum on ([m,n]). But for a non - closed interval (like ((a,b))) and without knowing continuity at the endpoints (since they are not in the domain), the function may or may not have absolute extreme values. Looking at the graph of (y = f(x)) on ((a,b)), there is no guarantee of attaining extreme values because the endpoints (a) and (b) (where extreme values could potentially be "approached" but not reached in the open interval) are not included.

Answer:

D. The function does not have any absolute extreme values on ((a,b)); B. Since the function (f) is continuous and the domain of (f) is not a closed interval, (f) may or may not have any absolute extreme values on its domain.