Find Global Extrema of Functions: Steps & Example

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  • Thread starter Thread starter Ali Asadullah
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SUMMARY

The discussion focuses on the steps to find global extrema of functions, specifically identifying critical points, evaluating function values at these points and endpoints, and determining the largest and smallest values to establish global maxima and minima. A key point raised is the relationship between endpoints and local extrema, emphasizing that endpoints are always local extrema. The behavior of the function at the endpoints determines whether they are classified as maxima or minima based on the function's increasing or decreasing nature.

PREREQUISITES
  • Understanding of critical points in calculus
  • Knowledge of function evaluation techniques
  • Familiarity with the concepts of maxima and minima
  • Basic grasp of increasing and decreasing functions
NEXT STEPS
  • Study the process of finding critical points in calculus
  • Learn how to evaluate functions at endpoints and critical points
  • Explore the relationship between local and global extrema
  • Investigate examples of functions with endpoints as local extrema
USEFUL FOR

Students and educators in calculus, mathematicians analyzing function behavior, and anyone interested in optimization techniques in mathematical functions.

Ali Asadullah
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Please check my steps for global extrema of functions.
1) Finding Critical points.
2) Finding values of f at critical points and end-points.
3) Checking which one is largest and which is smallest.
4) Largest would be Global maxima and the smallest would be minima.

Now a question, i know how to find global extrema if they are at
end-points. How can i find local extrema if they occur at end-points?
I will be thankful to you if you illustrate it with a simple example.
 
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Strictly speaking, and endpoint is always a "local extremum". If the function is increasing there, then the endpoint is either a max or a min depending on which side the interval is. If the function is decreasing, then that is reversed.
 

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