anonymous
  • anonymous
How many local max/ min does P(x) = x^57 + 7x^11 + 3x - 1000 has?
Mathematics
jamiebookeater
  • jamiebookeater
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ghazi
  • ghazi
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
anonymous
  • anonymous
the answer is 0
anonymous
  • anonymous
@ghazi answer is 0

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

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