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, # - x1 < x2, f(x1) > f(x2). ;, - % #
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x %
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. 3.13,
# : |
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*. 3.13. ' |
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# |
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4 ' 8 (7 &( ( #' " &( )# *).
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< %
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2 # D(y) = (–?; 0) (0; +?).
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y |
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, f(x) – # % (–?; 0) (0; +?).3 |
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2 D (y) = R. |
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# % x=0. < % .3
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2 ; y = 3 |
x % x=0, |
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1 |
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1.& # f(x).
2.& ( f '(x).
3.$ , :
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2 # D(y)=R.
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, : 0 2/5.
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*. 3.23. : y = (x − 1)3 x2
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f (−1) > 0 , |
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2 # D(y) = (–?; –1) (–1; +?). |
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y |
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x − 3 |
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x + 1 − x + 3 |
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x − 3 |
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= 2 x + 1 |
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x − 3 |
2 |
*. 3.24. : |
y = |
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1 x =3. , x= –1 # -
. , ymin = f (3) = 0 .3
3.36.+7 !$: +' : )# * " #
& % % # (
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% # ( ( , #
, # . 0- # ( # (
% ( , % # -
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+' : 8 $ )# * " #[ , b]:
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.
2.# x = , x = b.
3.& # # # ( (.
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4 |
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& # ( |
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y = |
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1 + x3 |
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2 & . y |
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8 |
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x3 , x = −1 |
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# - |
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f (−2) = 2 , |
f (−1) = −3 , |
f (−0,5) = 5 . |
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ymax = f (−0,5) = 5 , |
ymin = f (−1) = −3 .3 |
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[1; e]. |
' 2: & # ( ( y=x–2·ln x |
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2 |
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x − 2 |
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f (2) = 2 − 2ln 2 ≈ 0,6 , |
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2 y′ = 1 − |
= |
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(1) = 1, |
ymin = f (2) = 0,6 .3 |
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ymax = f |
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3.38. , # ! &($ #" 8 #( &($ 8 ) )# *. 4 8 #
! y=f(x) % ( ; b), -
( #- % . ! y=f(x) %
( ; b), -
( - #- % -
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. 3.25. , -
( ; b) (b; c).
!
# , ( . , = sin x ( . . 3.26)
(0; ,),
(,; 2,) .
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*. 3.27. ' |
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( ) |
* , - % , #
# .
4 ' 12. ) y=f(x) % ( ; b). 0-
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!
$
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2 & '' , . y' = –2x, y'' = –2 < 0 (–?; +?), , . 3
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2 y'' = ex > 0 #- x, . 3
*. 3.28. = 2 – x2. |
*. 3.29. = ex. |
*. 3.30. = x3. |
' 3: = x3 ( . . 3.30).
2 y'' = 6x, y'' < 0 x < 0 y'' > 0 x > 0. , x < 0
, x > 0 . 3
*. 3.31. '
, # ,
, % .
&, - , - %, %
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# – . $ , - % -
.
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# % # %.
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& -