Extreme Value Theorem for Constant Function y=1

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In summary, the Extreme Value Theorem is applicable for constant functions such as y=1, where the minimum and maximum values are found everywhere. This theorem states that the minimum of a function on a set A is the value m if there exists a in A such that f(a)=m, and m<=f(x) for all x in A. For example, if f(x)=11 for the interval [-10,10], then the minimum of f is 11 and is achieved for all x such that -10<=x<=10. Overall, the Extreme Value Theorem is useful for determining the minimum and maximum values of a function in a given set.
  • #1
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?
 
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  • #2
The minimum and maximum are every where.
Recall that we say m is the minimum of f on a set A if it is true that
there exist a in A such that
f(a)=m and
m<=f(x) for all x in A

If we have for example
f(x)=11 for [-10,10]
we would say f has minimum 11 on [-10,10]
depending what we were trying to do we would might further say
The minimum of f is 11 and is achived for all x such that -10<=x<=10.
 
  • #3
Thanx man! i got it.
 

FAQ: Extreme Value Theorem for Constant Function y=1

1. What is the Extreme Value Theorem for Constant Function y=1?

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.

2. How is the Extreme Value Theorem applicable to a constant function y=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.

3. Can the Extreme Value Theorem be used to find the exact maximum and minimum values of a constant function y=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.

4. What is the significance of the Extreme Value Theorem for Constant Function y=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.

5. Can the Extreme Value Theorem be applied to functions other than a constant function y=1?

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.

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