( ).
1. f (x).
2. f′(x) .
3. f″(x) f″(x) .
4. .
5. .
3. f (x) = 2x3 + 3 x2 - 12x + 5.
1. : (-¥, +¥).
2. f ′(x) = 6x2 + 6x - 12. f ′(x) = 0; 6(x2 + - 2) = 0 Þ = 1, = - 2.
3. f ″(x) = 12x + 6. f ″(1) = 18 > 0, f ″(- 2) = - 18 < 0.
4. x = 1 - , = - 2 - .
5. f max = f (- 2) = 2(- 2)3 + 3(- 2)2 - 12(- 2) + 5 = 25, f min = f (1) = - 2.
:
f'(x1) | f"(x1) | |
- | ||
+ | ||
y=f (x) [ b]. . , f (x) . [,b], , ( ), , . , .
, [,b] , , . : , , .
.
1. .
2. , [ a,b ].
3. , .. f(a), f(b).
4. , .2 .3, .
.
4
,
(a, b), .
,
(b, c), .
, , , .
. .