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.\nthe function has an absolute minimum at $x = c$ value but does not have an absolute maximum value on $(a,b)$\nthe function does not have any absolute extreme values on its domain\nexplain the results in terms of the extreme value theorem.\na. 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\nb. 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\nc. 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\nd. 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

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.\nthe function has an absolute minimum at $x = c$ value but does not have an absolute maximum value on $(a,b)$\nthe function does not have any absolute extreme values on its domain\nexplain the results in terms of the extreme value theorem.\na. 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\nb. 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\nc. 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\nd. 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

Answer

Brief Explanations:

The Extreme Value Theorem states that if a function ( f(x) ) is continuous on a closed interval ([m,n]), then ( f(x) ) attains an absolute maximum and an absolute minimum on ([m,n]). In this case, the domain ((a,b)) is an open interval (not closed), and even though the function may be continuous on parts of the interval, the lack of a closed - interval domain means there are no guarantees about the existence of absolute extrema.

Answer:

D. 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.