1
3 1-
12. 2013-2014 .
.
() (a,b), ( ).
x0, f(x0) , y=f(x) , .
( ). y=f(x) U(x0) x0 U(x0) x0.
1) U(x0) f ' (x)>0 <x0 f '(x)<0 x>x0, x0 ¾ ;
2) U(x0) f ' (x)<0 <x0 f '(x)>0 x>x0, x0 ¾ ;
3) U(x0) f ' (x)>0 f '(x)<0 x¹ x0, x0 ¾ .
y=f(x) 0 f''(x0) . , f ''(x0)>0, x0 - , f ''(x0)<0, x0 - .
y=f (x) (a,b).
y=f (x) () (a,b), x0Î(a,b) "Î(a,b) ( ) , (x0, f (x0)).
. y=f(x) (a,b). () , f ''(x)³0
(f ''(x) 0) "xÎ(a,b).
. 0 y = f (x), , 0, .. >x0, y-yk ³ 0, < x0, y-yk £ 0 . 0, , , 0
( ). y=f(x) U(x0)\{x0} 0. , .
0, f (x0) , f "(x0)=0 , .
( ). y = f (x) U(x0)\{x0} x0, x0 . , x<x0 x>x0, f ''(x) , x0 . x<x0 x>x0, f ''(x) , x0 .
. L k, M k L M (.. |OM| ¥) ( ). =0 y=f (x) , 0 0+ .
|
|
( ). y=kx+b () y=f (x) , ()
.
1. .
() [1,3-.163].
2. [ 2, 6.2; 4]. .
1. . [1, 3-.161].
:
- .
- .
- .
- .
- .
:
1. . ) ; ) ; ) ; D)
2. : y=x2+4x+5 A) 2; B) -2; C) 0; D) 6
3. .
A) ; B) ; C) $ D)
4. .
A) = 100; = -16; B) = 16; = -8;
C) = 8; = -12; D) = -12; = -16
5. : y=x2(1-x)
A. 0;-2 B.0; 2/3 C. 2;-2/3 D. 0;3/2
6. y=3x+ +5 x=0,5: A. -9 B.12 C.-12 D.9/4
ҚҚ | Ғ | ||
ө | Growth | ||
decrease | |||
critical | |||
maximum | |||
minimum | |||
өң | convexity | ||
concave | |||
ȳ | bend |
:
1. .. . . : ә, 2007. -408.
2. .., .. : .- .: , 2007, 2006
3. .., .., .. . , 1. , , 2003.
4. - . .. . . II-., , 2002.
:
5. .. 1. . : , 2008.
6. .., .. . . . Ȼ,2006. -479.