Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
!
"#$!%
!"# $%&%$'('
)*$+!,% !-
./0$1%2$'34$'
56(7-+4-89$:
1;!" <'=!">;
.4?)?+ !- .%?;
# %2.1 $4?(
@) 0$-$'(A!">;'
0$*$!,+#B4C;#:D%!E
0$F$ !- .4?43(A 0$1
%?:$!"4.$:GH )!
%;;I*-0$;6-5-
!-4(
J;4$$/!,:!,K
%2F:%?;87LM!@?7(((N*$+
$;817LO4F.-.>#)0$)#
+#B-81(
PQJ. !-:B%3;&4$3
F B? (#!4? >.;# B? ;(
R !-:;'4'# .*
>/I!S.;##T
FH$$.%?;S+$!,#
/5&'$?%?!$ !- !S%U.
Trang 1
Sng kin kinh nghim
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
c6?+:I$1 90$
$:3F:=61 90$% .4
4$H#4#$;(/5.4'O9
:%US0$0-"21 !!8h?4!"%>
%>d3(
gNF9P
_ !-:?4S XY-.:$$9$
!-:B%3;S +
H!!:;4".$ !-:$>;9
d!"$*$4>$-.P!!F9
!-:Z5 i #<)K%3;
:$!,$Z#41;'#SF)
$D#41(7!"= i #<!-!-$
!-:*S$F:;"?'0$
:'#[$$j(
_ kB#B9%?. !-:B%3;
!-/!, B? (
gl+H66!K%2 !- $:mH$
fYYnafYYo#..%?;$'9p4S XY' 2!P
qS r34!,!K%2 !-
XY`
X
J=f(nstRu(vst
:uu(Xsw#aRi$px(os
XY`
v
J=XstRnst
<)!, !-:!-!-(
_ R'FZ %3;
_ R:$!,$=6!SF$#41$
;(
_ J6! I3;z!,%?-.9
!-:B%3;(
_ J6d0${*4?#BM$1 9
;#%$S(
"
l.H1B;419$|4S !D
6 %24;#-.9%? !-:B%3;
3FH(A*$*!,::6#%?;5
'Z!%?1 ) I4? V, S.H
1B9/!,(r1 8%?/3 #)0$1
B1$)4$+8$B:D"
5:$?9+(
Trang 4
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
c6?'!"d;6!S%UK+|
4*0C#90$(r4$I .$
<$>#(';6> .559
$S.I1 )(
@). !-:B%3;';6>
> .*$!,+;6>-.P
gA*$!, i #<!-!- !-:B%3
;P
≥
gA*$+j
`\d^
`\d^
≥
=
−
A(x) neáu A(x) 0
neáu A(x)< 0
39
;P
`
`
` c ` c t ` c ` c t ` ( c `(c t
c c
+ > + − < − = =
Trang 5
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
` c ` c `(c Yt+ = + ⇔ ≥
gLI!,5+ i #<!-!- i #<)
!F !-:.(
c6?+;6>6'Z•1#!,+
%?-.9 !-:B%3;!,:;
XYD"! !- .2)/%?
A a
\f^(A!1;$9
!-:\f^4$9 !-:\X^(
\).0: !-#P
f f
\ ^
=
x
A a
!;
!"%US$ !-:1-^
N%2XPJ. !-:P
^
p u p− =x
^
p u− + = −x
J.P
^
p u p− =x
⇔
o
p
f
p
d
pd u p pd o
pd u p pd f
d
W\_u^6 !-:
p u− + = −x
'$(
• , /+
\ ^
\ ^=
x
A B x
‚L!- .P
Cch 1:
\ ^
f f
\ ^ \ ^
\ ^ Y
\ ^
=
≥
= ⇔
x
x x
A
A
B x
B x
B
≥
x
x
x
A
A
A
B x
B x
B x
B x
B x
N%2fPJ. !-:P
^
p f X− = +x x
\N%2]JR?XY-.uy^
^
v
f
f u u−+ = +x x x
J.P
rXP
( )
f X Y
p f X
f
f
p \f X^
p
f
f
p Y
p
+ −
≥ −
≥ −
⇔ ⇔ ⇔ =
= −
=
=
x
x
− = +
+ ≥
− = − +
X
d
f
fd X
d v
d v Y
f
d
X
p
fd X
d
f
pd f Y
f
d
p
− − =
⇔ =
≥ −
≥ −
− =
=
N1; !-:
p f X− = +x x
$$P
f
d
p
=
g7.V#.$!.B3•.$
B ..
^
v
f
f u u−+ = +x x x
v
f
f u u−+ = +x x x
v
v
x
v
v
f
f
+
⇔ ⇔
−
−
+ ≥
+ + ≥
+ = − +
− =
− + ≥
− + ≥ ∀ ∈
=
=
=
=
− + ≥ ∀ ∈
− + = (vo ânghieäm)
N1; !-:
v
f
f u u−+ = +x x x
$d€Yd€x
gA#K%2X4: !-#O ..$ !-:1
v3 B? (
Trang 8
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
• , 0+
` c
\d^ \d^
x y v v X+ + = − +x x x x
J.P
^
f f
\ \ ^X f u X^ f u⇔ =− = − − −x x x x
f f
d fd X vd fYd fu⇔ − + = − +
Y
f
pd Xod fv⇔ − + =
d v
d f
=
⇔
=
N1; !-:
X f u− = −x x
$Pd€fd€v
^
f f
x y v v X
f f
x y v v X
f f
u f XY Y
=
−
=
⇔
+ + =
x
x
x x (vo ânghieäm)
N1; !-:
f f
x y v v X+ + = − +x x x x
$P
f
p
−
=x
d€v
B
x
N%2vPJ. !-:P
^
f f
d pd v d fd p Y+ − + + − =
^
fd X d f Y− + − =
J.P
^
f f
d pd v d fd p Y+ − + + − =
f
d pd v Y
f
d fd p Y
+ − =
⇔
+ − =
d X
d v
d X
d X
d p
− =
=
⇔ ⇔
− =
=
\N'$)
N1; !-:
fd X d f Y− + − =
'$P
)1di;!,
fd X d f Y− + − =
fdaX€daf€Y\‚^
6'9d=$Z\‚^6 !-:
fd X d f Y− + − =
'
$
Trang 10
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
‚A I%?-.'!
%?>1%254??.P(
• , 2+
\ ^ \ ^ \ ^
+ =A B C
⇔ =
\'.di64?^
gA#
p d u− ≤ <
:
u−x
€uad
d p d p− = −
!-:\X^8P
\uad^g\dap^€pdaX
⇔
_pd€_y
d p⇔ =
\.di61^
gA#
d u≥
:
u−x
€dau
d p d p− = −
!-:\X^8P
\dau^g\dap^€pdaX
⇔
d€_X\'.di64?^
N1;$9 !-:\X^4d€p
Trang 11
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
^
p XX o− + − =x x
− − =
− − = −
J.XP
d f X u d f x− − = ⇔ − =
d f x \XŠ^
d f x \fŠ^
− =
⇔
− = −
J.XŠP
d f x d o− = ⇔ =
d o
d o
=
⇔
= −
J.fŠP
d f x d v− = − ⇔ = −
R'D?9d)
d v= −
J=v(pstRXY(xst
:vo(psw#aRi$px(os
)"456
6I;4$ !- !"!, %2). !-
:B%3;(;6K%2 !-
6 .!,45$, (k|$ !- 6
'!,F:. !-:'•(@F
34K%2 !- V, ?#.
3(N3F;=!">;$$.%?; .
# , $;F !- , (
k !- PQJ. !-:B%3;‹$
XYH$$.%?;'5!,$P
_!"d;6* 2+4>$.$ !-:
B%3;6 !-:?%2
)I*$+#B-.ŒjH.
d4". .*z(
Trang 13
1
Sng kin kinh nghim
Trn Quang T – Trưng THPT – Đnh An
_7 !- ./%? !-:B%3
; !,'2+:;$4?
, 4C$;$1 '$3"(@4 45
!,.;$:B!%;4?4$
4>$6$(
_…Œ 3:$ !-:F!S!,
P1%?!F !-:%?045
$ !- , 4C)$#..(
_q'4'S#B-.jH>#$|4?
!-: $4".?(