True or False. An absolute maximum or minimum must occur at a critical point or at an endpoint.
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For the reader's convenience, the critical values of a function are all values in which f ′ ( x ) = 0 and when f ′ ( x ) is undefined. At the endpoints of an interval, there can only be absolute extrema, as there is no turning point at the endpoint. However, inside this interval, the extrema present may be either absolute or relative. Thus we have the following statements:
I . If there is an extremum at an endpoint of an interval, that extremum must be absolute.
I I . If there is an extremum inside the interval, then the extremum can be either absolute or relative.