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lovekblue

  • 3 years ago

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

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  1. ghazi
    • 3 years ago
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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

  2. lovekblue
    • 3 years ago
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    the answer is 0

  3. lovekblue
    • 3 years ago
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    @ghazi answer is 0

  4. ghazi
    • 3 years ago
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    can you guess what could be the reason behind zero ?

  5. lovekblue
    • 3 years ago
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    no.. something about (0, -1000)

  6. ghazi
    • 3 years ago
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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

  7. ghazi
    • 3 years ago
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    @eliassaab sir, help

  8. lovekblue
    • 3 years ago
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    haha

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

  10. ghazi
    • 3 years ago
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    @lovekblue why are you laughing bro lol

  11. ghazi
    • 3 years ago
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    there you go @lovekblue

  12. ghazi
    • 3 years ago
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    @mukushla sorry forgot this

  13. lovekblue
    • 3 years ago
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    but P(x) starts from (0,-1000), wouldnt it cross 0 in some time?

  14. ghazi
    • 3 years ago
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    no, it would not it will tend to zero but won't cross zero

  15. lovekblue
    • 3 years ago
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    how do u know o_o

  16. ghazi
    • 3 years ago
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    check out the definition that muku has mentioned above

  17. lovekblue
    • 3 years ago
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    but what he talks about is P'(x)

  18. lovekblue
    • 3 years ago
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    P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...

  19. mukushla
    • 3 years ago
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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

  20. lovekblue
    • 3 years ago
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    ohh right

  21. ghazi
    • 3 years ago
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    |dw:1352269291734:dw| think of something like this

  22. lovekblue
    • 3 years ago
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    dont know why i suddenly related root to max/min.. i get it now thanks!

  23. mukushla
    • 3 years ago
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    np :)

  24. lovekblue
    • 3 years ago
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    thanks both of u :)

  25. ghazi
    • 3 years ago
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    :) special thanks to @mukushla

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