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