Extreme Value Theorem states that a function () which is found to be continuous over a closed interval [, ] is guaranteed to have extreme values in that interval. Given the graph of the function, identify the extrema (both minimum and maximum) of the given graphs below by giving the maximum and minimum point. If there is no extrema, provide an explanation. *
A. Maximum: (-2, 2); Minimum: (2,1)
B. Maximum: (2, -2); Minimum: (1,2)
C. No extrema because there is no absolute maximum and no absolute minimum value
D. No extrema because the curve is broken in its open interval (-2,2)
Answers & Comments
Answer:
D. No extrema because the curve is broken in its open interval (-2, 2)
Explanation:
According to the graph,
the function is an open interval (-2, 2)
So the function doesn't have extreme value. because there is no absolute maximum and no absolute minimum.