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4.3-bo'lim : Minimal va maksimal qiymatlar

  1. Quyida \(f\left( x \right)\) funksiyasining grafigi keltirilgan. Funksiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    This graph has five line segments to it. The first segment starts at (-10,6) and ends at (-6,-5). The second segment starts at (-6,-5) and ends at (-2,4). The third segment starts at (-2,4) and ends at (2,-1). The fourth segment starts at (2,-1) and ends at (4,8). The final segment starts at (4,8) and ends at (7,-6).
  2. Quyida \(f\left( x \right)\) funksiyasining grafigi keltirilgan. Funksiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    This graph starts at (-4, -8) and increases until it reaches a peak at (-3,0). It then decreases until it reaches a valley at (-2,-3). The curve then increases to a peak at (1,9) and then decreases to a valley at (5.5, -5). Finally, it increases until it reaches (7,3).
  3. Quyida \(f\left( x \right)\) funksiyasining grafigi keltirilgan. Funksiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    This graph starts at (-3, -3) and increases until it reaches a peak at (-1,1.5). It then decreases until it reaches a valley at (0,1). The curve then increases to a peak at (1,1.5) and then decreases until it reaches (3,-3).
  4. Quyida \(f\left( x \right)\) funksiyasining grafigi keltirilgan. Funksiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    This graph starts at (-10, -8) and increases until it reaches a peak at (-6,8) and then decreases until it hits (-4,4). The graph then jumps down to the point (-4,-2) and increases until it reaches the point (2,10). The graph then jumps down to the point (2,6) and decreases until it reaches a valley at (4,-10) and then increases until it reaches (5,-6).
  5. \(f\left( x \right) = 3 - {\frac{1}{2}}x\) grafigini chizing va quyidagi intervallarning har birida funksiyaning barcha nisbiy ekstremal va mutlaq ekstremalarini aniqlang.
    1. \(\left( { - \infty ,\infty } \right)\)
    2. \(\left[ { - 3,2} \right]\)
    3. \(\left[ { - 4,1} \right)\)
    4. \(\left( {0,5} \right)\)
  6. \(g\left( x \right) = {\left( {x - 2} \right)^2} + 1\) grafigini chizing va quyidagi intervallarning har birida funktsiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    1. \(\left( { - \infty ,\infty } \right)\)
    2. \(\left[ {0,3} \right]\)
    3. \(\left[ { - 1,5} \right]\)
    4. \(\left[ { - 1,1} \right]\)
    5. \(\left[ {1,3} \right)\)
    6. \(\left( {2,4} \right)\)
  7. \(h\left( x \right) = {{\bf{e}}^{3 - x}}\) grafigini chizing va quyidagi intervallarning har birida funktsiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang.
    1. \(\left( { - \infty ,\infty } \right)\)
    2. \(\left[ { - 1,3} \right]\)
    3. \(\left[ { - 6, - 1} \right]\)
    4. \(\left( {1,4} \right]\)
  8. \(h\left( x \right) = \cos \left( x \right) + 2\) grafigini chizing va quyidagi intervallarning har birida funksiyaning barcha nisbiy ekstremal va mutlaq ekstremallarini aniqlang. Hammasi bu muammo uchun radyanlarda ishlaydi.
    1. \(\left( { - \infty ,\infty } \right)\)
    2. \(\left[ {\displaystyle - \frac{\pi }{3},\frac{\pi }{4}} \right]\)
    3. \(\left[ {\displaystyle - \frac{\pi }{2},2\pi } \right]\)
    4. \(\left[ {\displaystyle \frac{1}{2},1} \right]\)
  9. \(x = 5\)da mutlaq maksimalga va \(x = 4\)da mutlaq minimumga ega bo‘lgan funksiya grafigini \(\left[ {3,9} \right]\) oralig‘ida chizing.
  10. \(x = 5\)da mutlaq minimumga, \(x = 0\) va \(x = 10\)da mutlaq maksimalga ega bo‘lgan funksiya grafigini \(\left[ {0,10} \right]\) oralig‘ida chizing.
  11. \(x = - 7\) da nisbiy minimumga, \(x = 2\) da nisbiy maksimalga va mutlaq ekstremaga ega bo‘lmagan funksiya grafigini \(\left( { - \infty ,\infty } \right)\) oralig‘ida chizing.
  12. Quyidagi shartlarga javob beradigan funksiya grafigini chizing:
    1. Kamida bitta mutlaq maksimalga ega.
    2. Bitta nisbiy minimumga ega.
    3. Mutlaq minimumga ega emas.
  13. Quyidagi shartlarga javob beradigan funksiya grafigini chizing:
    1. \(\left[ {2,9} \right]\) oralig'ida chizilgan.
    2. Intervalgacha bir nuqtada ichki uzilish bor.
    3. Qisman uzilishda mutlaq maksimalga ega (b).
    4. Qisman uzilishda mutlaq minimumga ega (b).
  14. Quyidagi shartlarga javob beradigan funksiya grafigini chizing:
    1. \(\left[ { - 4,10} \right]\) oralig'ida chizilgan.
    2. Nisbiy ekstremal yo'q.
    3. Bitta oxirgi nuqtada mutlaq maksimalga ega.
    4. Boshqa oxirgi nuqtada mutlaq minimumga ega.
  15. Quyidagi shartlarga javob beradigan funksiya grafigini chizing:
    1. Bir nuqtada uzilish bor.
    2. Mutlaq maksimal va mutlaq minimumga ega.
    3. Har qanday mutlaq ekstremal uzilishda yuzaga kelmaydi.