�e�te n�sleduj�c� �lohy na absolutn� extr�my funkc�.
$$
\gather
z(x,y) = x^2 + 12xy + 2y^2; \, M = \{ [x,y], 4x^2 + y^2 = 1 \}; \\
u(x,y,z) = x - 2y + 2z; \, M = \{ [x,y,z], x^2 + y^2 + z^2 = 1, \,
x+y+z = 0 \};
\\
f(x,y,z) = xyz; \, M = \{ [x,y,z], x^2 + y^2 + z^2 = 1 \}; \\
u(x,y,z) = xy^2z^3; \, M = \{[x,y,z]; x + 2y + 3z = a, x >0, y >0 \}
   \text{; kde } a > 0; \\
u(x_1, x_2, \dots, x_n) = x_1^p + x_2^p + \dots + x_n^p; \, \\
M = \{ [x_1, x_2, \dots, x_n]; x_1 + x_2 + \dots + x_n = a; x_1 >
0, x_2 > 0, \dots, x_n > 0 \}; \text{ kde } a>0, p > 1; \\
u(x,y,z) = \sin {x} \sin {y} \sin {z}; \, M = \{[x,y,z]; x + y +z = {\pi
   \over 2}, x > 0, y > 0, z >0 \}.
\endgather
$$
