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. determine whether the function has any absolute extreme values on (a, b). choose the correct choice below. a. the function has an absolute maximum value at x = c and an absolute minimum value at x = b on (a, b). b. the function has an absolute maximum value at x = c but does not have an absolute minimum value on (a, b). c. the function has an absolute minimum value at x = b but does not have an absolute maximum value on (a, b). d. the function does not have any absolute extreme values on (a, b).
Answer
Explanation:
Step1: Analyze the graph for absolute maximum
Looking at the graph, there is a highest point at (x = c) within the interval ((a,b)), so the function has an absolute maximum at (x = c).
Step2: Analyze the graph for absolute minimum
The left - hand limit as (x) approaches (a) and the right - hand limit as (x) approaches (b) do not reach a lowest point within the open interval ((a,b)) (since the endpoints (a) and (b) are not included in the open interval ((a,b))).
Answer:
B. The function has an absolute maximum value at (x = c) but does not have an absolute minimum value on ((a,b))