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

Question

ghazi · Answer

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 · Answer

the answer is 0

anonymous · Answer

@ghazi  answer is 0

ghazi · Answer

can you guess what could be the reason behind zero ?

anonymous · Answer

no.. something about (0, -1000)

ghazi · Answer

i am unable to think why it has answer zero , i don't think so , let me call my friend @mukushla  buddy help

ghazi · Answer

@eliassaab  sir, help

anonymous · Answer

haha

anonymous · Answer

hello

because P(x) is a strictly increasing function since$$P'(x)=57x^{56}+77x^{10}+3>0$$

ghazi · Answer

@lovekblue  why are you laughing bro lol

ghazi · Answer

there you go @lovekblue

ghazi · Answer

@mukushla  sorry forgot this

anonymous · Answer

but P(x) starts from (0,-1000), wouldnt it cross 0 in some time?

ghazi · Answer

no, it would not it will tend to zero but won't cross zero

anonymous · Answer

how do u know o_o

ghazi · Answer

check out the definition that muku has mentioned above

anonymous · Answer

but what he talks about is P'(x)

anonymous · Answer

P'(x) is strictly increasing.. that doesnt help saying it wont cross 0...

anonymous · Answer

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 · Answer

ohh right

ghazi · Answer

|dw:1352269291734:dw| think of something like this

anonymous · Answer

dont know why i suddenly related root to max/min..
i get it now thanks!

anonymous · Answer

np :)

anonymous · Answer

thanks both of u :)

ghazi · Answer

:) special thanks to @mukushla