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

1. 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

2. lovekblue

3. lovekblue

4. ghazi

can you guess what could be the reason behind zero ?

5. lovekblue

6. ghazi

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

7. ghazi

@eliassaab sir, help

8. lovekblue

haha

9. mukushla

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

10. ghazi

@lovekblue why are you laughing bro lol

11. ghazi

there you go @lovekblue

12. ghazi

@mukushla sorry forgot this

13. lovekblue

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

14. ghazi

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

15. lovekblue

how do u know o_o

16. ghazi

check out the definition that muku has mentioned above

17. lovekblue

but what he talks about is P'(x)

18. lovekblue

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

19. mukushla

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

20. lovekblue

ohh right

21. ghazi

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

22. lovekblue

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

23. mukushla

np :)

24. lovekblue

thanks both of u :)

25. ghazi

:) special thanks to @mukushla