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How many local max/ min does P(x) = x^57 + 7x^11 + 3x  1000 has?
 one year ago
 one year ago
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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ghaziBest ResponseYou've already chosen the best response.4
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

ghaziBest ResponseYou've already chosen the best response.4
can you guess what could be the reason behind zero ?
 one year ago

lovekblueBest ResponseYou've already chosen the best response.0
no.. something about (0, 1000)
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
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

mukushlaBest ResponseYou've already chosen the best response.2
hello because P(x) is a strictly increasing function since\[P'(x)=57x^{56}+77x^{10}+3>0\]
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
@lovekblue why are you laughing bro lol
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
@mukushla sorry forgot this
 one year ago

lovekblueBest ResponseYou've already chosen the best response.0
but P(x) starts from (0,1000), wouldnt it cross 0 in some time?
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
no, it would not it will tend to zero but won't cross zero
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
check out the definition that muku has mentioned above
 one year ago

lovekblueBest ResponseYou've already chosen the best response.0
but what he talks about is P'(x)
 one year ago

lovekblueBest ResponseYou've already chosen the best response.0
P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...
 one year ago

mukushlaBest ResponseYou've already chosen the best response.2
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

ghaziBest ResponseYou've already chosen the best response.4
dw:1352269291734:dw think of something like this
 one year ago

lovekblueBest ResponseYou've already chosen the best response.0
dont know why i suddenly related root to max/min.. i get it now thanks!
 one year ago

ghaziBest ResponseYou've already chosen the best response.4
:) special thanks to @mukushla
 one year ago
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