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

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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 xz3 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 z20; 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 z12; 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 z45; 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
+ xz5 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.
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