Question

Find any critical numbers of the function. (4x)/(x^2+1)

Answer 1

\[\frac{ 4x }{ x ^{2}+1}\] is the equation.

Answer 2

what you want?

Answer 3

We are working on applications of differentiation, specifically extremums. What I learned is you first take the derivative, then figure out when it equals zero or is undefined. The numbers where it equal zero or is undefined is what I'm looking for.

Answer 4

you want to i make drive of your equation?

Answer 5

(u/v)' = (u'v-v'u)/(v^2)

Answer 6

by get u=4x and v=x^2+1 solve it

Answer 7

ok?

Answer 8

Well actually I did that, but you just made me think of what I forgot to do and why it's all messed up- I forgot the 'du' of the derivative part of 'x^2 +1'! Thanks! Haha

Answer 9

Wait, I lied.... it doesn't need a "du". I'm not sure what I did wrong still to get the bizarre results that I got... Can you go through all of it in steps for me?

Answer 10

I know how to do the derivative, I just think that maybe somewhere along the lines I made a mistake that I'm having trouble catching because the ending equations that I got were just incredibly weird. The only way I could possibly solve them is with i.

Answer 11

( 4(x^2+1)-2x(4x) )/( (x^2+1)^2)

Answer 12

Okay, I've got that part.

Answer 13

Next, I have simplified it to \[\frac{ -4x ^{2}+4 }{ (x^{2}+1)^{2} }\]

Answer 14

Is that right?

Answer 15

yes

Answer 16

Okay, that's good, but when I set the bottom to equal zero- like (x^2+1)^2=0 - it ends up to x^2=-1, and you can't take a square root of -1. :/ So I'm not sure what's up with that.

Answer 17

x^2=-1
x=i=sqr(-1)

Answer 18

But I don't think that we can use i, so that's what I'm wondering about.

Answer 19

if you write question correctly the answer is
x=i

Answer 20

Okay, thanks!

Answer 21

your welcome