.
4.15.1 .
¢ () > 0 (,b), () .
¢ () < 0 (,b), () .
: . 0 , ¢() = 0.
, . .
:
¢ 0 + -, 0 .
¢ 0 -
+, 0 .
, .
, ( ), .
4.15.3.
1. f ¢().
2. f ¢() = 0.
3. 1, 2 n , . .
4. , .
5. .
4.16.1.
1. f¢ ().
2. f ¢() = 0 1, 2,
3. f ² ().
4. f ² (1) < 0, ,
f ² (1) > 0, ,
f ² (1) = 0, .
¢¢ () > 0 (, b). () , , .
¢¢ () < 0 (,b), () , , .
, ¢¢() = 0 , .
, ( ), .
|
|
4 2
= 2 16 ,
.
1. :
¢ = 2 16
2. ( ) : ¢= 0, 2 16 = 0, = 8. 2:
2( 8) = 0.
3. , = 8
< 8, , 7 . -. , <8.
> 8, , 9 , +. , >8.
- + ( ), = 8.
4. :
= 82 128 = 64 128 = - 64.
(8, - 64) , .
5. , , ¢= 2 -16. ¢¢ = 2. , .
4.17.
= f(), (1, 1) :
1 = f ¢ (1) ( 1),
k1 1 .
= f() (1,1) , . :
k2 = -
4.18.
y=kx + b y =f(x) +¥,
(f (x) kx b) = 0
, k = , b = .
k = 0, : = b ( ).
= , . .
4.19.
1. ;
2. ;
3. ;
4. , . , , . .
5. . , , ;
6. . ;
7. . . . ,
8. . .
|
|
9. . , .
10. ;
11. .
2
14
:
1. y = 2 sin x 8. = sin x cos x
2. y = x3 ×cosx 9. y = e sin x
3. y = x× tgx 10. y = lnx× sin x
4. y = x5 ex 11. y = 2 ×cos x
5. y = x2 ×lnx 12. y = e ×cosx
6. y = x 3 2 13. y = tgx× e
7. y = x2 ×ctgx 14. y = 3 × e
:
1. = sinx/ x2 8. y = sinx/cosx
2. y = cosx/ x3 9. y = cosx/sinx
3. y = tgx/ x 10. y = e x / sinx
4. y = ex / x3 11. y = 3 x / cosx
5. y = 2 / x 12. y = tgx/ 2x
6. y = lnx/ x3 13. y = x 4 / 2 x
7. y = x5 /sinx 14. y = x/ sinx
t:
1. S = 3t + t3 + 7 t = 3 8. S = 2t3 + 4t2 + 5 t = 1
2. S = 4 + 2t + t4 t = 1 9. S = 3t2 + t3 + 6 t = 2
3. S = 9 + 3t + 2t3 t = 3 10. S = 3t3 + 4t2 + 5 t = 1
4. S = 8 + t2 + 2t3 t = 2 11. S = 5t2 + 2t3 + 9 t = 2
5. S = 9 + 2t2 + t3 t = 2 12. S = 4t2 + 8 + t3 t = 3
6. S = 5t2 + 4t3 t = 3 13. S = t3 + 9 + 3t2 t = 2
7. S = 7 + t3 + 5t2 t = 4 14. S = t4 + 8 + 4t t = 2
, :
1. = ( + 2)2 ( 4)
2. = ( + 3)2 ( - 6)
3. = ( + 4)2 ( 5)
4. = ( + 1)2 ( - 5)
5. = ( - 5)2 ( + 1)
6. = ( + 2)2 ( 7)
7. = ( 2)2 ( 5)
8. = ( -7)2 ( + 2)
9. = ( + 5)2 ( 4)
10. = ( 8)2 ( + 1)