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

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ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4number 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

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4can you guess what could be the reason behind zero ?

lovekblue
 3 years ago
Best ResponseYou've already chosen the best response.0no.. something about (0, 1000)

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4i am unable to think why it has answer zero , i don't think so , let me call my friend @mukushla buddy help

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

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4@lovekblue why are you laughing bro lol

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4@mukushla sorry forgot this

lovekblue
 3 years ago
Best ResponseYou've already chosen the best response.0but P(x) starts from (0,1000), wouldnt it cross 0 in some time?

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4no, it would not it will tend to zero but won't cross zero

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4check out the definition that muku has mentioned above

lovekblue
 3 years ago
Best ResponseYou've already chosen the best response.0but what he talks about is P'(x)

lovekblue
 3 years ago
Best ResponseYou've already chosen the best response.0P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.2not 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

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4dw:1352269291734:dw think of something like this

lovekblue
 3 years ago
Best ResponseYou've already chosen the best response.0dont know why i suddenly related root to max/min.. i get it now thanks!

ghazi
 3 years ago
Best ResponseYou've already chosen the best response.4:) special thanks to @mukushla
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