Suppose that f(x,y,z)\displaystyle {f{{\left({x},{y},{z}\right)}}} = (x−2)2+(y−2)2+(z−2)2\displaystyle {\left({x}-{2}\right)}^{{2}}+{\left({y}-{2}\right)}^{{2}}+{\left({z}-{2}\right)}^{{2}} with 0≤x,y,z\displaystyle {0}\le{x},{y},{z} and x+y+z≤10\displaystyle {x}+{y}+{z}\le{10}.
  1. The critical point of f(x,y,z)\displaystyle {f{{\left({x},{y},{z}\right)}}} is at (a,b,c)\displaystyle {\left({a},{b},{c}\right)}. Then
    a=\displaystyle {a}=  
    b=\displaystyle {b}=  
    c=\displaystyle {c}=  
  2. Absolute minimum of f(x,y,z)\displaystyle {f{{\left({x},{y},{z}\right)}}} is  
    and absolute maximum is   .

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