f (x) = 3 3 2 + 3 +5.
f¢ (x) = 3 2 6 + 3. г f¢ (x) = 0 = 1, f¢ (1) = 0. ,
.
, f ¢(1) = f ²(1) = 0, f ²¢(1) ¹ 0. = 1 f (x) .
4. f (x) 0, . :
1) f ²¢( 0) > 0, f (x) 0 ;
2) f ²¢( 0) < 0, f (x) 0 ;
3) f ² ( 0) = 0, 0 , .
. f ²¢( 0) > 0, , , 0 (f ¢( 0) = 0),
.
0 , 0, x < x 0 f¢ (x) < 0, x> x 0 f¢ (x) > 0 . 0 f (x) , 2 0 .
f (x) 0, f ²¢( 0) < 0.
f (x) = 6.
f¢ (x) = 6 5. : = 0.
1) 2 = 0 f¢ (x) . , = 0 f (x) .
2) 3 f ¢¢ () = 30 4, f ²¢() = 120 3, f (4)(x) = 360 2, f (5)(x) = 720 , f (6)(x) = 720, f ¢(0) = f ²(0) = f ²¢(0) = 0, f (6)(0) = 720 > 0. 6 , 3 = 0 f (x) .
3) f ¢(0) = 0, f ²(0) = 0, 4 = 0.
4) . | | > 0 ¹ 0 |0| = 0, 6 = 0 = 0, f (x) = 6 = 0 .
, f (x) , .
5.6.10.
( )
1. . , , .
. f (x) [ a; b ], (a; b) .
f (x) [ a; b ].
1. f¢ (x) = 0, Î(a; b), ( ).
|
|
2. f (x) [ a; b ] ( , ).
3. . f (x) [ a; b ].
[0,01; 100].
● [0,01; 100] = 0,2. = 0,2 [0,01; 100]:
.
.