Extreme Value Theorem for Constant Function y=1

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SUMMARY

The Extreme Value Theorem applies to constant functions, such as y=1, where both the maximum and minimum values are constant across the entire domain. For a constant function f(x)=11 defined on the interval [-10, 10], the minimum value is 11, achieved for all x within that interval. This demonstrates that the theorem holds true, as the minimum and maximum values exist and are equal throughout the specified set.

PREREQUISITES
  • Understanding of the Extreme Value Theorem
  • Basic knowledge of constant functions in calculus
  • Familiarity with function notation and intervals
  • Concept of minimum and maximum values in mathematical analysis
NEXT STEPS
  • Study the implications of the Extreme Value Theorem on non-constant functions
  • Explore examples of continuous functions and their extrema
  • Learn about the Mean Value Theorem and its relationship to the Extreme Value Theorem
  • Investigate applications of the Extreme Value Theorem in optimization problems
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Students of calculus, mathematics educators, and anyone interested in understanding the properties of functions and their extrema in mathematical analysis.

vikcool812
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How is Extreme Value theorem correct for a constant function such as y=1 , where is the maximum and minimum?
 
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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.
 
Thanx man! i got it.
 

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