The extreme values theorem does not apply, and f(x) has a maximum but not a minimum. Option D is correct.
A graph has shown in the image, It is to determine whether the extreme value theorem applies.
What is a graph?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
The extreme value theorem comprises that if a function is continuous on a defined interval [a,b], then the function must have a maximum and a minimum in the interval. Since in the graph the function does not have the minimum and is not defined for the closed interval. The function has a maximum on the left side of the graph but starts with the discontinuity on the left side so the Extreme value theorem does not hold.
Thus, The extreme values theorem does not apply, and f(x) has a maximum but not a minimum.
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