Local Extreme Values over subdomains

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I consider a $f(x,y)$ function which is continuous on the domain $X=[0,1]times [0,1]$. I am trying to find local extreme values of the $f(x,y)$ function by splitting the whole domain $X$ into small subdomains. For instance, let's consider subdomains $X'=[0,.1]times[0,.1]$ and $X''=[0,.2]times[0,.2]$. Let us denote the maximum value of the function $f(x,y)$ over the subdomain $X'$ and $X''$ by $M'$ and $M''$, respectively. It turns out that $M'>M''$. Does it make sense for any function?
$$P.S.$$ Extreme values are estimated with Wolfram Mathematica.




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    I consider a $f(x,y)$ function which is continuous on the domain $X=[0,1]times [0,1]$. I am trying to find local extreme values of the $f(x,y)$ function by splitting the whole domain $X$ into small subdomains. For instance, let's consider subdomains $X'=[0,.1]times[0,.1]$ and $X''=[0,.2]times[0,.2]$. Let us denote the maximum value of the function $f(x,y)$ over the subdomain $X'$ and $X''$ by $M'$ and $M''$, respectively. It turns out that $M'>M''$. Does it make sense for any function?
    $$P.S.$$ Extreme values are estimated with Wolfram Mathematica.




    maxima-minima




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      I consider a $f(x,y)$ function which is continuous on the domain $X=[0,1]times [0,1]$. I am trying to find local extreme values of the $f(x,y)$ function by splitting the whole domain $X$ into small subdomains. For instance, let's consider subdomains $X'=[0,.1]times[0,.1]$ and $X''=[0,.2]times[0,.2]$. Let us denote the maximum value of the function $f(x,y)$ over the subdomain $X'$ and $X''$ by $M'$ and $M''$, respectively. It turns out that $M'>M''$. Does it make sense for any function?
      $$P.S.$$ Extreme values are estimated with Wolfram Mathematica.




      maxima-minima




      share|cite|improve this question













      I consider a $f(x,y)$ function which is continuous on the domain $X=[0,1]times [0,1]$. I am trying to find local extreme values of the $f(x,y)$ function by splitting the whole domain $X$ into small subdomains. For instance, let's consider subdomains $X'=[0,.1]times[0,.1]$ and $X''=[0,.2]times[0,.2]$. Let us denote the maximum value of the function $f(x,y)$ over the subdomain $X'$ and $X''$ by $M'$ and $M''$, respectively. It turns out that $M'>M''$. Does it make sense for any function?
      $$P.S.$$ Extreme values are estimated with Wolfram Mathematica.





      maxima-minima





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      share|cite|improve this question




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      edited Jul 27 at 7:27
























      asked Jul 27 at 7:16









      David

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