26

  1. Amp; 37. ³ '.
  2. II. ³
  3. IV. ²²Ͳ ²
  4. V. ²²Ͳ ̲
  5. . . . ?
  6. . . .

.

46.1 ( ). N (x0; y0) z = ? (; ) , : ? 'x(0; 0) = 0, ? 'y(0; 0) = 0.

. , , = 0. ? (; 0) = ? () , = 0. , (. . 25.4), ? '(0) = 0, . . ?'x (0; y0) = 0.

, ? 'y(0; 0) = 0.

? 'x(0; 0) = 0 ? 'y(0; 0) = 0 , z = ? (; ) , ? (; ), , . . г z = z0(. (45.2)).

. , . , (0; 0) (. . 211), .

, z ? ? (; ) , . . F 'x= 0, f 'y= 0, z.

, , .

, . г , . , , z = . (0; 0) ( z 'x= z 'y- ). z = , . . (0; 0) z> 0 ( I III ) z <0 ( II IV ).

, .

46.2 ( ). (; ) ? (; ) . (0; 0) A = f ''xx(x0; y0), = ? ''xy(0; 0), = ? ''y(0; 0).

:

1. ?> 0, ? (; ) (0; 0) : , <0; , > 0;

2. ? <0, ? (; ) (0; 0) .

? = 0 (0; 0) , . .

.

46.1. z = 32- 3- 4.

г: z 'x= -32, Z 'y= 32-43. , , .

, :

M1(6; 3) 2(0; 0).

: z ''X= 6-6, z ''x= 6, z ''y= -122.

1(6; 3) : = -18, = 36, = -108,

-2= -18 - (- 108) -362 = 648, . . ?> 0.

<0, 1 : zmax= Z (6; 3) = 3-36-3-63-34 = 324-216-81 = 27.

2(0; 0): = 0, = 0, = 0 , , ? = 0. . z 2 : z (0; 0) = 0. , z = -4<0 = 0, ? 0; z = 3> 0 <0, = 0. , 2(0; 0) z , . , 2 .



24 | 27

³ 9. | 10 | 12 | 13 | 14 | 16 | 20 | 21 | 22 | 23 |

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