lovekblue
How many local max/ min does P(x) = x^57 + 7x^11 + 3x - 1000 has?
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ghazi
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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
lovekblue
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the answer is 0
lovekblue
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@ghazi answer is 0
ghazi
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can you guess what could be the reason behind zero ?
lovekblue
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no.. something about (0, -1000)
ghazi
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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
ghazi
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@eliassaab sir, help
lovekblue
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haha
mukushla
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hello
because P(x) is a strictly increasing function since\[P'(x)=57x^{56}+77x^{10}+3>0\]
ghazi
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@lovekblue why are you laughing bro lol
ghazi
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there you go @lovekblue
ghazi
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@mukushla sorry forgot this
lovekblue
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but P(x) starts from (0,-1000), wouldnt it cross 0 in some time?
ghazi
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no, it would not it will tend to zero but won't cross zero
lovekblue
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how do u know o_o
ghazi
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check out the definition that muku has mentioned above
lovekblue
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but what he talks about is P'(x)
lovekblue
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P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...
mukushla
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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
lovekblue
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ohh right
ghazi
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|dw:1352269291734:dw| think of something like this
lovekblue
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dont know why i suddenly related root to max/min..
i get it now thanks!
mukushla
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np :)
lovekblue
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thanks both of u :)
ghazi
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:) special thanks to @mukushla