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vikcool812
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How is Extreme Value Theorm correct for a constant function such as y=1 , where is the maximum and minimum?
The Extreme Value Theorem states that for a continuous function, a closed interval will have both a maximum and a minimum value. In the case of a constant function y=1, the maximum and minimum values will both be 1.
The Extreme Value Theorem is applicable to a constant function y=1 because it is a continuous function and therefore satisfies the conditions of the theorem. This means that a closed interval of the form [a, b] will have a maximum and minimum value of 1.
Yes, the Extreme Value Theorem can be used to find the exact maximum and minimum values of a constant function y=1. Since the function is continuous, the maximum and minimum values will occur at the endpoints of the interval, which can be easily determined as 1.
The Extreme Value Theorem for Constant Function y=1 serves as a mathematical proof that a constant function has both a maximum and minimum value within a closed interval. This is important for understanding the behavior of functions and their values within a given interval.
Yes, the Extreme Value Theorem can be applied to any continuous function. It states that a closed interval will always have both a maximum and minimum value for a continuous function. This applies to functions other than a constant function y=1.