¿ç¿¿ëýõ õè÷ýýë
Transcript of ¿ç¿¿ëýõ õè÷ýýë
ÕÈ×ÝÝË 28 Õ¿çãà 1á
2009-11-10
Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóëàõ
Çîðèëã
î
2.Ôóíêöèéí òóõàé
îéëãîëòûã öîãö áàéäëààð ýçýìøèõ
3.Ôóíêöèéí óëàìæëàë
àøèãëàí ãðàôèê áàéãóóëæ
ñóðàõ
1. Ôóíêöèéã øèíæèëæ
ñóðàõ
Çîðèëò1.
Ôóíêöèéí òîäîðõîéëîã
äîõ ìóæ îëæ ñóðàõ
4. Ôóíêöèéí õàìãèéí èõ áà áàãà
óòãà îëæ , ãðàôèê
áàéãóóëàõ
Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóëàõ
1-áàã•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
2-áàã
•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
3-áàã
•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
2 33y x x
3 23 1y x x
3 23 2y x x
Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóëàõ
4-áàã
•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
5-áàã
•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
6-áàã
•Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
3 23 9y x x x
2 48 2y x x
4 22 4y x x
Æèøýý: ôóíêèéã øèíæèëæ ãðàôèê áàéãóóëüÿ.
4 28y x x
1. Ôóíêöèéí òîäîðõîéëîãäîõ ìóæ îëîõ
Ôóíêöèéí àðãóìåíòèéí îðîíä îðëóóëàí òàâèõàä óòãàòàé áàéëãàäàã òîîíóóäûí îëîíëîãèéã òîäîðõîéëîãäîõ ìóæ ãýíý.1. ò.ì 2. ò.ì 3. ò.ì 4. ò.ì
Ä¿ðýì Áîäîëò:
y x 0xlgy x 0x 1
yx
0x y x ;
;x
4 28y x x
2. Óëàìæëàë îëíî
1.2.3.4.5.6.
7.
Ä¿ðýì Áîäîëò:
0c1x
1n nx n x u v u v u v u v u v u v v u
2
u u v v u
v v
4 2
3
8
4 16
y x x
x x
3. Ñýæèãòýé öýãèéã îëíî.
Óëàìæëàëûã îëæ òýãòýé òýíö¿¿ëæ áîäîæ îëíî.
Ä¿ðýì Áîäîëò:
3
2
2
2
4 16 0
(4 16) 0
0
4 16
4
2
2
x x
x x
x
x
x
x
x
4. Çàâñàðóóäàä õóâààæ, òýìäýã òàâèíà.
- Êîîðäèíàòûí øóëóóí äýýð ñýæèãòýé öýãýý òýìäýãëýí çàâñàðóóäàä õóâààíà.-Çàâñàð áîëãîíîîñ äóðûí öýã àâ÷ óëàìæëàëûí óòãûã îëæ òýìäýãýý òàâèíà.
Ä¿ðýì Áîäîëò:
3
3
3
3 4 3 16 3 108 48 60
1 4 1 16 1 4 16 12
1 4 1 16 1 4 16 12
2 4 27 16 3 108 48 60
y
y
y
y
34 16y x x
5. Ôóíêöèéí ºñºõ áóóðàõûã òîãòîîíî
+ òýìäýãòýé áîë òýð çàâñàð ôóíêö ºñíº……………..- Òýìäýãòýé áîë òýð çàâñàð ôóíêö áóóðíà.
1. Çàâñàðò (-) ó÷èð áóóðíà.2. Çàâñàðò (+) ó÷èð ºñíº.3. Çàâñàðò (-) ó÷èð áóóðíà4. Çàâñàðò (+) ó÷èð ºñíº.
Ä¿ðýì Áîäîëò:
;2 2;0 0;2
2;
6.max, min îëîõ
(-) ààñ (+) ð¿¿ øèëæèæ áàéâàë min-òàé.-------------(+) ýýñ (-) ð¿¿ øèëæèæ áàéâàë max-òàé
Ä¿ðýì Áîäîëò:
2 0 2
- + - +
-16 0 -16
min max min
f x
f x
;2
2;0 0;2 2;
4 2
4 2
( 2) ( 2) 8 ( 2) 16 32 16
(0) 0
(2) 2 8 2 16 32 16
y
y
Y
4 28y x x
8.Ãðàôèê áàéãóóëàõ
(-2;-16)(2;-16)(0;0)öýã¿¿äèéãÒýìäýãëýæ,ºñºõ
áóóðàõòýìäýãèéã õàðæ
çóðíà.
Ä¿ðýì Áîäîëò
Ôóíêöèé øèíæèëæ ãðàôèê áàéãóóëàõäàà:
1.Ôóíêöèéí òîäîðõîéëîãäîõ
ìóæ îëíî.
2. Óëàìæëàë îëíî.
3. Ýêñðåìóì öýã îëíî.
4. Çàâñàðóóäàä õóâààæ
òýìäýãýý îëíî.
5.ªñºõ áóóðàõ çàâñàðûã
òîãòîîíî
6. max, min îëíî.
7. Ýêñòåìóì öýã äýýð ôóíêöèéí
óòãûã îëíî
8. Ãðàôèê áàéãóóëíà.
Ãýðèéí äààëãàâàð
Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
Äàðààãèéí õè÷ýýë äýýð ñýäâèéí øàëãàëò àâíà.
4 2
5 2
15 4.5
21
45
y x x
y x x