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lovekblue Group Title

How many local max/ min does P(x) = x^57 + 7x^11 + 3x - 1000 has?

  • one year ago
  • one year ago

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  1. ghazi Group Title
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    number of roots of first differentiation decides total number of minima and maxima , after one differentiation you will get highest order of 56 so it will have 56 roots and therefore total number is 56

    • one year ago
  2. lovekblue Group Title
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    the answer is 0

    • one year ago
  3. lovekblue Group Title
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    @ghazi answer is 0

    • one year ago
  4. ghazi Group Title
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    can you guess what could be the reason behind zero ?

    • one year ago
  5. lovekblue Group Title
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    no.. something about (0, -1000)

    • one year ago
  6. ghazi Group Title
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    i am unable to think why it has answer zero , i don't think so , let me call my friend @mukushla buddy help

    • one year ago
  7. ghazi Group Title
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    @eliassaab sir, help

    • one year ago
  8. lovekblue Group Title
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    haha

    • one year ago
  9. mukushla Group Title
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    hello because P(x) is a strictly increasing function since\[P'(x)=57x^{56}+77x^{10}+3>0\]

    • one year ago
  10. ghazi Group Title
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    @lovekblue why are you laughing bro lol

    • one year ago
  11. ghazi Group Title
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    there you go @lovekblue

    • one year ago
  12. ghazi Group Title
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    @mukushla sorry forgot this

    • one year ago
  13. lovekblue Group Title
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    but P(x) starts from (0,-1000), wouldnt it cross 0 in some time?

    • one year ago
  14. ghazi Group Title
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    no, it would not it will tend to zero but won't cross zero

    • one year ago
  15. lovekblue Group Title
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    how do u know o_o

    • one year ago
  16. ghazi Group Title
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    check out the definition that muku has mentioned above

    • one year ago
  17. lovekblue Group Title
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    but what he talks about is P'(x)

    • one year ago
  18. lovekblue Group Title
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    P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...

    • one year ago
  19. mukushla Group Title
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    not P'(x) but P(x) is strictly increasing (why?) and P(x) is continous ...so there are no local Max or Min but there is a one root

    • one year ago
  20. lovekblue Group Title
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    ohh right

    • one year ago
  21. ghazi Group Title
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    |dw:1352269291734:dw| think of something like this

    • one year ago
  22. lovekblue Group Title
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    dont know why i suddenly related root to max/min.. i get it now thanks!

    • one year ago
  23. mukushla Group Title
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    np :)

    • one year ago
  24. lovekblue Group Title
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    thanks both of u :)

    • one year ago
  25. ghazi Group Title
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    :) special thanks to @mukushla

    • one year ago
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