1. y =x − x +
6 8 2
ôóíêöèéí ºñºõ áà áóóðàõ
çàâñðûã îëíî óó
y f(x)=x^2-6x+8
12
10
ýíäýýñ õàðàõàä
8
ºñºõ çàâñàð íü
3 ààñ ∞ áàéíà.
6
Õàðèí áóóðàõ
4
çàâñàð íü
2 - ∞ ààñ 3
áàéíà. x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-2
-4
-6

2. Ñýäýâ
Óëàìæëàëûí òóñëàìæòàéãààð
ôóíêöèéí ºñºõ áà áóóðàõ çàâñðûã
îëîõ

3. Çîðèëãî
Ôóíêöèéí óëàìæëàëûã àøèãëàí ò¿¿íèé
ºñºõ áà áóóðàõ çàâñðûã ÷ºëººòºé îëæ
ñóðàõ

4. çîðèëò
Ôóíêöèéí ãðàôèêèéí òóõàéí öýã äýýðõ
ø¿ðãýã÷èéí ºíöãèéí êîýôôèöåíòûã ñóäëàõ
Ôóíêöèéí óëàìæëàë íü òýãýýñ áàãà áàéõ, òýãýýñ
èõ áàéõ, òýãòýé òýíö¿¿ áàéõ íºõöë¿¿äèéã ñóäëàõ
Ñóäëàñàí ç¿éë¿¿äýä ä¿ãíýëò ºãºõ
Ãàðãàñàí ä¿ãíýëòýý àøèãëàí áîäëîãî áîäîõ
àëãîðèòì çîõèîõ
Äàñãàë àæèëëàõ
¯íýëãýý ä¿ãíýëò ºãºõ

5. y = x − 6x + 8 2 ôóíêöèéí ãðàôèêèéí
ø¿ðãýã÷ øóëóóíóóäûã
ñîíèðõî¸
y f(x)=x^2-6x+8
Click to edit Master text styles f(x)=4x-17
12
Second level
●
Third level
10
●
Fourth level
8
●
Fifth level
6
4
2
x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-2
-4
-6

6. Ôóíêöèéí ãðàôèêèéí
ø¿ðãýã÷ øóëóóíû ºíöãèéí
êîýôôèöåíò íü
k = f ( x0 ) = tgα
'
ї ї нд : α < 90 бол, tgα > 0
0
α > 90 бол, tgα < 0.байдаг
0

7. y f(x)=x^2-6x+8
f(x)=4x-17
12 f(x)=6x-28
f(x)=2x-8
10
8
6
4
α < 90 бa, tgα > 0
0
тул. f ( x0 ) > 0
'
2
x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-2
-4
-6

8. y f(x)=x^2-6x+8
f(x)=-2x+4
12 f(x)=-4x+7
f(x)=-6x+8
10
8
6
4
α > 90 бa, tgα < 0
0
тул. f ( x0 ) < 0
'
2
x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-2
-4
-6

9. y f(x)=x^2-6x+8
y=0x-1
12
10
8
6
4
α = 0 бa, tgα = 0
0
тул. f ( x0 ) = 0
'
2
x
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13
-2
-4
-6

10. ýíäýýñ õàðàõàä
ôóíêöèéí ºñºõ çàâñàð áîëîõ 3 ààñ ∞ ûí
õîîðîíä áàéõ öýã¿¿äýä òàòñàí ø¿ðãýã÷
øóëóóíóóä íü îõ òýíõëýãòýé õóðö ºíöºã
¿¿ñãýõ áà f ' ( x0 ) > 0 áàéíà. Õàðèí
áóóðàõ çàâñàð áîëîõ - ∞ ààñ 3 ûí
õîîðîíä áàéõ öýã¿¿äýä òàòñàí ø¿ðãýã÷
øóëóóíóóä íü îõ òýíõëýãòýé ìîõîî ºíöºã
¿¿ñãýõ áà f ' ( x0 ) < 0 áàéíà. Èéìýýñ
àëèâàà ôóíêöèéí óëàìæëàëûí ýåðýã óòãàòàé
áàéõ çàâñàðò ôóíêö ºñºæ, õàðèí ñºðºã
óòãàòàé áàéõ çàâñàðò ôóíêö áóóðäàã
áàéíà.Õýðýâ ôóíêöèéí óëàìæëàë òýãòýé
òýíö¿¿ áîë f ' ( x0 ) = 0 áàéõ áà ýíý
¿åèéí öýãèéã òîãòâîðæèëòûí öýã ãýäýã

11. Óëàìæëàëûí òóñëàìæòàéãààð ôóíêöèéí ºñºõ
áà áóóðàõ çàâñðûã îëîõ áîäëîãî áîäîõäîî
Ôóíêöèéí óëàìæëàëûã îëîõ
Óëàìæëàëûã òýãòýé òýíö¿¿ëæ
òîãòâîðæèëòûí öýãèéã îëîõ
òîãòâîðæèëòûí öýãèéã òîîí øóëóóíä
áàéðëóóëæ óëàìæëàëûí òýìäãèéã
èíòåðâàëûí àðãààð îëîõ
Îëñîí çàâñàðóóäààð ºñºõ áà áóóðàõ
çàâñðûã òîãòîîñíîîð áîäëîãî
áîäîãäîíî