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

Question

Determine from the given graph weather the function has any absolute extreme values on [a,b], then expplain how your answer is consistent with the extreme values theorem

Determine from the given graph whether the function has amy absolute extreme values on [a, b]. Then explain how your answer is consistent with the extreme value theorem. 10 y =f(x) a c1 c2 b Determine whether the function has any absolute extreme values on [a, b]. Choose the correct answer below. A. The function has an absolute minim urm value x =c2 but does not have an absolute maximum value on [a, b]. O B. The function has an absolute maximum value atx-c1 but does not have an absolute minimum value on [a, b ° C. The function has an absolute maximum value atx-b and an absolute minimum value at x =c2 on a, b] OC. The function has an absolute maximum value at x -b and an absolute minimum value atx 2 on [a, b O D. The function does not have any absolute extreme values on [a, b]. Explain the results in terms of the extreme value theorem. O A. 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. B. Since the function f is continuous and the domain of fis not a closed interval, f may or may not have an absolute xtreme values on its domain O C. 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. D. 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.

Explanation / Answer

f has absolute maximum at x=b

f has absolute minimum at x=c2

where b, c2 both on belongs to open interval a,b

so first one answer 'C'

since the function is continuous on closed interval a,b , so f ahs absolute maximum and absolute minimum on its domain

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