1. =3-3.
:
1. ;
2. , ( );
3. , ;
4. ;
5. ;
6. , ( );
7. , ;
8. ;
9. ;
10. .
, .. . , , .
.
1.
2. lim (x 3 -3 x)=- ¥; lim (x 3 -3 x)=+ ¥,
x - ¥ x + ¥
3. . , f ¢ (x)>0. f ¢ (x) =32-3 > 0, 2 >1 ||> 1. , =2-3 , f ¢ (x)<0: 32-3 < 0, 2 < 1, -1 < < 1. , =3-3 ]-1, 1[.
4. . (x)=3 x 2 -3=0 : 1=-1, 2=1. 1=-1, 2=1. 1=-1 , f ¢ (x)=302-3<0. =-1 , =-1 . f (-1)=(-1)3-3(-1)=2 ( . 4). 2=1 , . , =1 . ( . 4).
5. : . f (0)=03-30=0 ( . 4).
. , < 0. , . , > 0. , .
7. . :
0); (0; 0), 0).
8. :
-1 | 0 | 1 | |||
f(x) | 2 | 0 | -2 | 0 | 0 |
0 | -3 | 0 | |||
-6 | 0 | 6 | |||
9. =3-3
4. =3-3.
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2. , , = k (100 x 2 - x 3), k -, - +=100.
. : = k (200-32)=0, 1=0, 2=200/3. 1=0: 1=0 . 2=200/3: , 2=200/3 , 2=100-200/3=33,3. , 33,3% .
2. , .. . , = f (x)= x 2 (a - x), - . ?
. : 1=0, 2=2/3.
1=0 , . 2=2/3: , 2=2/3 . , =2/3 , .