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функцийг шинжилж график байгуулах

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функцийг шинжилж график байгуулах

  1. 1. Çîðèëãî 1. Ôóíêöèéã øèíæèëæ ñóðàõ 2.Ôóíêöèéí òóõàé îéëãîëòûã öîãö áàéäëààð ýçýìøèõ 3.Ôóíêöèéí óëàìæëàë àøèãëàí ãðàôèê áàéãóóëæ ñóðàõ
  2. 2. 2. Ôóíêöèéí óëàìæëàë, ñý æèãòýé öýã îëæ ñóðàõ 3. Ôóíêöèéí ºñºõ, áóóðàõûã òîãòîîõ 1. Ôóíêöèéí òîäîðõîéëîãäîõ ìóæ îëæ ñóðàõ
  3. 3. Ôóíêöèéг øèíæèëæ ãðàôèê áàéãóóëàõäàà: 1.Ôóíêöèéí òîäîðõîéëîãäîõ ìóæ îëíî. 6. max, min îëíî. 7. Ýêñòåìóì öýã äýýð ôóíêöèéí óòãûã îëíî 2. Óëàìæëàë îëíî. 5.ªñºõ áóóðàõ çàâñàðûã òîãòîîíî 8. Ãðàôèê áàéãóóëíà. 3. Ýêñðåìóì öýã îëíî. 4. Çàâñàðóóäàä õóâààæ òýìäýãýý îëíî.
  4. 4. y x 4 8x 2
  5. 5.  Ä¿ðýì Ôóíêöèéí àðãóìåíòèéí îðîíä îðëóóëàí òàâèõàä óòãàòàé áàéëãàäàã òîîíóóäûí îëîíëîãèéã òîäîðõîéëîãäîõ ìóæ ãýíý. x ò.ì x 0 1. y 2. y lg x ò.ì x  0 3. y 1 ò.ì x 0 x ; 4. y x ò.ì  Áîäîëò: x y x 4 ; 8x 2
  6. 6.  Ä¿ðýì  1. c 0 2. x 1 3. x n n xn 1 4. u v u v 5. u v u v 6. u v uv vu 7. u v uv vu v2 Áîäîëò: y 4x x 3 4 16 x 8x 2
  7. 7.  Ä¿ðýì  4 x3 Óëàìæëàëûã îëæ òýãòýé òýíö¿¿ëæ áîäîæ îëíî. 16 x Áîäîëò: x (4 x 2 16) x 0, x1 0 4x2 x2 x2 x3 y 0 0 0 Үед сэжигтэй цэгийг олно. 16 4 2 2 x1 0 x2 2 x3 2
  8. 8.  Ä¿ðýì - Êîîðäèíàòûí øóëóóí äýýð ñýæèãòýé öýãýý òýìäýãëýí çàâñàðóóäàä õóâààíà. -Çàâñàð áîëãîíîîñ äóðûí öýã àâ÷ óëàìæëàëûí óòãûã îëæ òýìäýãýý òàâèíà. y Áîäîëò: y 3 4 3 y 1 4 1 3 3 4x 3 16 x 16 3 108 48 16 1 4 16 12 y 1 4 13 16 1 4 16 y 2 4 27 16 3 108 48 60 12 60
  9. 9.  Ä¿ðýì + òýìäýãòýé áîë òýð çàâñàð ôóíêö ºñíº - Òýìäýãòýé áîë òýð çàâñàð ôóíêö áóóðíà.  1. 2. 3. 4. Áîäîëò: ;2 Çàâñàðò (-) ó÷èð áóóðíà. 2;0 0;2 2; Çàâñàðò (+) ó÷èð ºñíº. Çàâñàðò (-) ó÷èð áóóðíà Çàâñàðò (+) ó÷èð ºñíº.
  10. 10.  Ä¿ðýì (-) ààñ (+) ð¿¿ øèëæèæ áàéâàë min ------------(+) ýýñ (-) ð¿¿ øèëæèæ áàéâàë max  Áîäîëò: y x4 8x2 ; 2 f x -2 2;0 0 - 0 + 0 0;2 - 2 0 -16 0 -16 min f x max min y ( 2) ( 2) 4 8 ( 2) 2 16 32 y (0) 0 Y (2) 24 8 22 16 32 16 16 2; +
  11. 11. (-2,8;-16) (2,8;-16) (0;0) öýã¿¿äèéã тýìäýãëýæ ºñºõ áóóðàõ òýìäýãèéã õàðæ çóðíà. y 0 2 2,8 -2,8 -2 -16 x
  12. 12. Ôóíêöèéг øèíæèëæ ãðàôèê áàéãóóëàõäàà: 1.Ôóíêöèéí òîäîðõîéëîãäîõ ìóæ îëíî. 6. max, min îëíî. 7. Ýêñòåìóì öýã äýýð ôóíêöèéí óòãûã îëíî 2. Óëàìæëàë îëíî. 5.ªñºõ áóóðàõ çàâñàðûã òîãòîîíî 8. Ãðàôèê áàéãóóëíà. 3. Ýêñðåìóì öýã îëíî. 4. Çàâñàðóóäàä õóâààæ òýìäýãýý îëíî.
  13. 13. 1-áàã y 3x 2 x 3 • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë. y x 3 3x 2 1 2-áàã • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë. y x3 3x 2 2 3-áàã • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
  14. 14. 4-áàã 8 2x2 y x4 • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë. 5-áàã y x 3 3x 2 9x • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë. 6-áàã y x 4 2x 2 4 • Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë.
  15. 15. Ãýðèéí äààëãàâàð Ôóíêöèéã øèíæèëæ ãðàôèê áàéãóóë. y y 1 4 x 2 1 5 x 5 5x2 4.5 4x2 Äàðààãèéí õè÷ýýë äýýð ñýäâèéí øàëãàëò àâíà.

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