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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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
the answer is 0
@ghazi answer is 0

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Other answers:

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

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