Дифференциальное исчисление функций нескольких переменных. Скляренко В.А - 52 стр.

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ВлГУ | Владимир

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1. F(x, y, z)= x
2
+ 2 y
2
+ z
2
+ 6 + 3 yz + z; x
0
= 0, y
0
= 3, z
0
= −4.
2. F(x, y, z)= 3 x
2
− y
2
+ z
2
+ 1 + 12 xz + 5 yz + 9 z; x
0
= −4, y
0
= 5, z
0
= 2.
3. F(x, y, z)= 2 x
2
− y
2
+ z
2
− 9 − 3 yz + 2 z; x
0
= 0, y
0
= 3, z
0
= −2.
4. F(x, y, z)= −y
2
+ 2 yz + 3 x
2
+ 6 xz + z
2
+ z; x
0
= −1, y
0
= 1, z
0
= 1.
5. F(x, y, z)= 2 y
2
+ yz − 2 x
2
+ z
2
+ 3 z − 32; x
0
= 0, y
0
= 2, z
0
= −8.
6. F(x, y, z)= −y
2
− yz + 6 x
2
− 3 xz + z
2
− 14; x
0
= 1, y
0
= −2, z
0
= 4.
7. F(x, y, z)= 7 y
2
+ 5 x
2
+ 2 xz + z
2
− 3 z − 5; x
0
= −1, y
0
= 0, z
0
= 5.
8. F(x, y, z)= −11 y
2
+ 2 x
2
+ 14 xz + z
2
− 40 z + 14; x
0
= 7, y
0
= 0, z
0
= −2.
9. F(x, y, z)= 7 y
2
+ 8 x
2
+ 24 xz + z
2
+ 30 z + 8; x
0
= −3, y
0
= 0, z
0
= 2.
10. F(x, y, z)= 2 y
2
+ 3 yz − 5 x
2
+ 5 xz + z
2
+ 12 z + 30; x
0
= −2, y
0
= 3,
z
0
= −4.
11. F(x, y, z) = −7 y
2
− 14 yx + x
2
+ 2 xz + 3 z
2
+ 8 z − 120; x
0
= 1,
y
0
= −1, z
0
= −8.
12. F(x, y, z)= 2 y
2
+ 4 yx + x
2
+ 2 xz + 3 z
2
+ 7 z − 11; x
0
= 1, y
0
= −1, z
0
= 1.
13. F(x, y, z)= 5 y
2
+10 yx+ x
2
+2 xz−3 z
2
+7 z+16; x
0
= 1, y
0
= −1, z
0
= 4.
14. F(x, y, z)= 3 y
2
+ 6 yx + x
2
+ 2 xz+ 7 z
2
− 5 z−20; x
0
= 1, y
0
= −1, z
0
= 2.
15. F(x, y, z)= −y
2
−2 yx+ x
2
−2 xz+5 z
2
+3 z−12; x
0
= −1, y
0
= 1, z
0
= −2.
16. F(x, y, z)= y
2
− 3 yx + x
2
+ xz − 2 z
2
+ 7 z + 10; x
0
= 2, y
0
= 3, z
0
= 5.
17. F(x, y, z)= 2 y
2
+ 3 yx + x
2
+ xz − 7 z
2
+ 13 z − 8; x
0
= 4, y
0
= −3, z
0
= 1.
18. F(x, y, z)= −y
2
+ yx + x
2
+ xz+ 8 z
2
− 30 z−45; x
0
= −2, y
0
= −1, z
0
= 5.
19. F(x, y, z)= 3 y
2
− 3 yx + x
2
+ xz− 7 z
2
− 10 z+4 2; x
0
= 6, y
0
= 3, z
0
= −3.
20. F(x, y, z)= y
2
+ 3 yx + x
2
+ xz + 2 z
2
− 4 z − 35; x
0
= 2, y
0
= −3, z
0
= 5.
21. F(x, y, z)= 4 y
2
+5 yx+ x
2
+ xz−5 z
2
+30 z+ 99; x
0
= 8, y
0
= −5, z
0
= 9.
22. F(x, y, z)= −y
2
− yx + x
2
+ xz + 6 z
2
− 20 z − 45; x
0
= −2, y
0
= 1, z
0
= 5.
23. F(x, y, z)= 3 y
2
+ 4 yx + x
2
+ xz + z
2
− 15 z + 32; x
0
= 6, y
0
= −4, z
0
= 4.
24. F(x, y, z)= y
2
+ 4 yx + 2 yz + 2 x
2
+ 3 z
2
+ 7 z − 11; x
0
= −1, y
0
= 1, z
0
= 1.
25. F(x, y, z)= y
2
+10 yx+2 yz+5 x
2
−3 z
2
+7 z+16; x
0
= −1, y
0
= 1, z
0
= 4.
26. F(x, y, z)= −y
2
+ yx − 4 yz + 6 x
2
+ 2 xz − z
2
− 3; x
0
= 0, y
0
= −2, z
0
= 1.
27. F(x, y, z)= −y
2
+ yx + 6 yz + 2 x
2
− 3 xz − z
2
− 8; x
0
= 0, y
0
= 3, z
0
= 1.
52
 1. F(x, y, z) = x2 + 2 y2 + z2 + 6 + 3 yz + z;      x0 = 0, y0 = 3, z0 = −4.
 2. F(x, y, z) = 3 x2 − y2 + z2 + 1 + 12 xz + 5 yz + 9 z;      x0 = −4, y0 = 5, z0 = 2.
 3. F(x, y, z) = 2 x2 − y2 + z2 − 9 − 3 yz + 2 z;     x0 = 0, y0 = 3, z0 = −2.
 4. F(x, y, z) = −y2 + 2 yz + 3 x2 + 6 xz + z2 + z;      x0 = −1, y0 = 1, z0 = 1.
 5. F(x, y, z) = 2 y2 + yz − 2 x2 + z2 + 3 z − 32;     x0 = 0, y0 = 2, z0 = −8.
 6. F(x, y, z) = −y2 − yz + 6 x2 − 3 xz + z2 − 14;      x0 = 1, y0 = −2, z0 = 4.
 7. F(x, y, z) = 7 y2 + 5 x2 + 2 xz + z2 − 3 z − 5;     x0 = −1, y0 = 0, z0 = 5.
 8. F(x, y, z) = −11 y2 + 2 x2 + 14 xz + z2 − 40 z + 14;       x0 = 7, y0 = 0, z0 = −2.
 9. F(x, y, z) = 7 y2 + 8 x2 + 24 xz + z2 + 30 z + 8;       x0 = −3, y0 = 0, z0 = 2.
10. F(x, y, z) = 2 y2 + 3 yz − 5 x2 + 5 xz + z2 + 12 z + 30;         x0 = −2, y0 = 3,
    z0 = −4.
11. F(x, y, z) = −7 y2 − 14 yx + x2 + 2 xz + 3 z2 + 8 z − 120;                x0 = 1,
    y0 = −1, z0 = −8.
12. F(x, y, z) = 2 y2 + 4 yx + x2 + 2 xz + 3 z2 + 7 z − 11;     x0 = 1, y0 = −1, z0 = 1.
13. F(x, y, z) = 5 y2 +10 yx + x2 +2 xz−3 z2 +7 z+16;          x0 = 1, y0 = −1, z0 = 4.
14. F(x, y, z) = 3 y2 + 6 yx + x2 + 2 xz+ 7 z2 − 5 z− 20;      x0 = 1, y0 = −1, z0 = 2.
15. F(x, y, z) = −y2 −2 yx+x2 −2 xz+5 z2 +3 z−12;             x0 = −1, y0 = 1, z0 = −2.
16. F(x, y, z) = y2 − 3 yx + x2 + xz − 2 z2 + 7 z + 10;        x0 = 2, y0 = 3, z0 = 5.
17. F(x, y, z) = 2 y2 + 3 yx + x2 + xz − 7 z2 + 13 z − 8;      x0 = 4, y0 = −3, z0 = 1.
18. F(x, y, z) = −y2 + yx + x2 + xz+ 8 z2 − 30 z− 45;         x0 = −2, y0 = −1, z0 = 5.
19. F(x, y, z) = 3 y2 − 3 yx + x2 + xz− 7 z2 − 10 z+ 42;       x0 = 6, y0 = 3, z0 = −3.
20. F(x, y, z) = y2 + 3 yx + x2 + xz + 2 z2 − 4 z − 35;        x0 = 2, y0 = −3, z0 = 5.
21. F(x, y, z) = 4 y2 +5 yx + x2 + xz−5 z2 +30 z+99;           x0 = 8, y0 = −5, z0 = 9.
22. F(x, y, z) = −y2 − yx + x2 + xz + 6 z2 − 20 z − 45;        x0 = −2, y0 = 1, z0 = 5.
23. F(x, y, z) = 3 y2 + 4 yx + x2 + xz + z2 − 15 z + 32;      x0 = 6, y0 = −4, z0 = 4.
24. F(x, y, z) = y2 + 4 yx + 2 yz + 2 x2 + 3 z2 + 7 z − 11;     x0 = −1, y0 = 1, z0 = 1.
25. F(x, y, z) = y2 +10 yx +2 yz+5 x2 −3 z2 +7 z+16;           x0 = −1, y0 = 1, z0 = 4.
26. F(x, y, z) = −y2 + yx − 4 yz + 6 x2 + 2 xz − z2 − 3;       x0 = 0, y0 = −2, z0 = 1.
27. F(x, y, z) = −y2 + yx + 6 yz + 2 x2 − 3 xz − z2 − 8;        x0 = 0, y0 = 3, z0 = 1.

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