Use the technique of constrained optimization (not calculus) to find the absolute maximum and minimum values of the function

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Name: Use the technique of constrained optimization (not calculus) to find the absolute maximum and minimum values of the function , for .
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Question

Use the technique of constrained optimization (not calculus) to find the absolute maximum and minimum values of the function 
  
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The Answer of Use the technique of constrained optimization (not calculus) to find the absolute maximum and minimum values of the function 
  
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Use the Technique of Constrained Optimization (Not Calculus) to Find