Determine from the given graph whether the function has any absolute extreme val

Question

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. y fix) Determine whether the function has any absolute extreme values on (a, b). Choose the correct answer below. ? A. The function has an absolute minimum at x-c value but does not have an absolute maximum value on (a, b). O B. The function has an absolute maximum value at x b but does not have an absolute minimum value on (a, b). O C. The function has an absolute maximum value at x b and an absolute minimum value at x c on (a, b). O D. The function does not have any absolute extreme values on its domain Explain the results in terms of the extreme value theorem. O A. Since the function fis continuous on a dlosed interval, attains both an absolute maximum value and an absolute minimum value on its domain. B Since the function f is not continuous and the domain off is a closed interval f may or may not have any absolute extreme values on its OC. Since the function f OD. Since the function fis not continuous and the 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. domain of f is not a closed interval, fmay or may not attain any absolute extreme values on its domain.

Explanation / Answer

Ans

i) D is true. The function doesnt have any absolute extreme values on its domain.

ii) D is true. Since the function is not continous (discontinuity at x = c) and the domain of f is (a,b) not a closed interval, by extreme value theorem f may or may not attaiin any absolute extreme values on its domain.

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