Suppose that f(x,y)=x2−xy+y2−4x+4y\displaystyle {f{{\left({x},{y}\right)}}}={x}^{{2}}-{x}{y}+{y}^{{2}}-{4}{x}+{4}{y} with D={(x,y)∣0≤y≤x≤4}\displaystyle {D}={\left\lbrace{\left({x},{y}\right)}{\mid}{0}\le{y}\le{x}\le{4}\right\rbrace}.
  1. The critical point of f(x,y)\displaystyle {f{{\left({x},{y}\right)}}} restricted to the boundary of D\displaystyle {D}, not at a corner point, is at (a,b)\displaystyle {\left({a},{b}\right)}. Then a=\displaystyle {a}=  
    and b=\displaystyle {b}=  
  2. Absolute minimum of f(x,y)\displaystyle {f{{\left({x},{y}\right)}}} is  
    and absolute maximum is   .

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