Online Course Discussion Forum

Maximums and Boundary Values

 
 
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Maximums and Boundary Values
by Tina Jin - Tuesday, 16 January 2024, 9:01 PM
 

Hello,

In some inequalities like Cauchy-Schwarz and AM-GM, the maximum/minimum value cannot be obtained by the variables. In such cases, what should I do to solve the problem? I was told something about boundary values and how that will be the max/min but the function is not necessarily monotonically increasing or decreasing, and it would be hard to tell at which intervals it will be monotonically increasing or decreasing.

Thanks,

Tina Jin

 
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Re: Maximums and Boundary Values
by Dr. Kevin Wang - Friday, 19 January 2024, 10:47 PM
 

This depends on specific problem.  In case the related function is monotonically increasing or decreasing in the interval, the boundary points are the ones to check.  Otherwise we have to find other properties.