## isabellaxochitl 2 years ago what are the critical numbers of f(x)= 4x/(x^2 +1)?

1. dpaInc

did u already calculate the derivative?

2. dpaInc

what's f ' (x) = ??

3. Goten77

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4. isabellaxochitl

do i simplify it further or just set it to 0 now?

5. Goten77

to simplify makes setting it = to 0 much easier

6. isabellaxochitl

ok i need help simplifying it…i don't think i am doing it right so far

7. Goten77

k also the critical points are what makes the top part become 0 .. or what makes the bottom part not exist.. in this case all reals exist on the domain... so we just gotta worry bout setting the top = to 0

8. isabellaxochitl

so i just completely forget the bottom part?

9. Goten77

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10. Goten77

i wouldnt say forget bout the bottom part... but usually in the 1st derivative test its worthless.. unless theres a square root or something that might make it non existiant

11. Goten77

hmm let me think... i gotta make sure i didnt say soemthing wrong

12. isabellaxochitl

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13. isabellaxochitl

wait wait that was wrong i got it its 1

14. Goten77

k i also need to add that critical points are when the derivative = 0 on the bottom or top.. and when its undefined... but it must all be in the domain

15. Goten77

We say that x=c is a critical point of the function f(x) if exists and if either of the following are true. f'(c)=0 or doesnt exist

16. Goten77

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17. Goten77

but ultimately the 1 and -1 are the critical points... sorry i kinda am lost in calculus *been a while since i did it* but making the top = to 0 and finding where stuff doesnt exist is where critical points are.... srry if i say something wrong but this info should be correct

18. isabellaxochitl

thanks for the help!