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ÔÓÍÊÖÈÉÃ ØÈÍÆÈËÆ ÃÐÀÔÈÊ ÁÀÉÃÓÓËÀÕ

Õèчýýë 19

Çîðèëãî

1. Ôóíêöèéã øèíæèëæ ñóðàõ

2.Ôóíêöèéí òóõàé

îéëãîëòûã öîãö áàéäëààð ýçýìøèõ

3.Ôóíêöèéí óëàìæëàë

àøèãëàí ãðàôèê áàéãóóëæ

ñóðàõ

ÇÎÐÈËÒ

1. Ôóíêöèéí òîäîðõîéëîãäîõ ìóæ îëæ ñóðàõ

2. Ôóíêöèéí óëàìæëàë, ñýæèãòýé öýã îëæ ñóðàõ

3. Ôóíêöèéí ºñºõ,

áóóðàõûã òîãòîîõ

Ôóíêöèéг øèíæèëæ ãðàôèê áàéãóóëàõäàà:

1.Ôóíêöèéí òîäîðõîéëîãäîõ

ìóæ îëíî.

2. Óëàìæëàë îëíî.

3. Ýêñðåìóì öýã îëíî.

6. max, min îëíî.

5.ªñºõ áóóðàõ çàâñàðûã

òîãòîîíî

4. Çàâñàðóóäàä

õóâààæ òýìäýãýý îëíî.

7. Ýêñòåìóì öýã äýýð ôóíêöèéí

óòãûã îëíî

8. Ãðàôèê áàéãóóëíà.

4 28y x x Æèøýý:

ôóíêèéã øèíæèëæ ãðàôèê áàéãóóëüÿ.

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

1. Ôóíêöèéí òîäîðõîéëîãäîõ

ìóæ îëîõ

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

2. Óëàìæëàë îëíî

3. ÑÝÆÈÃÒÝÉ ÖÝÃÈÉÃ ÎËÍÎ.

Óëàìæëàëûã îëæ òýãòýé òýíö¿¿ëæ áîäîæ îëíî.

Үед сэжигтэй цэгийг олно.

Ä¿ðýì Áîäîëò:

3

2

1

2

2

2

3

4 16 0

(4 16) 0

0, 0

4 16

4

2

2

x x

x x

x x

x

x

x

x

1

2

3

0

2

2

x

x

x

0y

4. ÇÀÂÑÀÐÓÓÄÀА ТЭМДЭГЛЭ

- 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. ФУНКЦИЙН ӨСӨХ БУУРАХ ЗАВСАРЫГ ОЛНО.

+ 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. ЭКСТРЕМУМЫГ ОЛНО.

(-) ààñ (+) ð¿¿ øèëæèæ áàéâàë min-------------(+) ýýñ (-) ð¿¿ øèëæèæ áàéâàë max

Ä¿ðýì Áîäîëò:

-2 0 2

- 0 + 0 - 0 +

-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

x-2 2

0

y

-16

-2,8 2,8

(-2,8;-16) (2,8;-16)(0;0) öýã¿¿äèéã тýìäýãëýæ ºñºõ áóóðàõ òýìäýãèéã õàðæ çóðíà.

Ôóíêöèéг øèíæèëæ ãðàôèê áàéãóóëàõäàà:

1.Ôóíêöèéí òîäîðõîéëîãäîõ

ìóæ îëíî.

2. Óëàìæëàë îëíî.

3. Ýêñðåìóì öýã îëíî.

6. max, min îëíî.

5.ªñºõ áóóðàõ çàâñàðûã

òîãòîîíî

4. Çàâñàðóóäàä

õóâààæ òýìäýãýý îëíî.

7. Ýêñòåìóì öýã äýýð ôóíêöèéí

óòãûã îëíî

8. Ãðàôèê áàéãóóëíà.

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

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