Question

Intervals of increase and decrease of x^2/(x^4+1)

Answer 1

calc?

Answer 2

yes

Answer 3

I have it graphed and everything

Answer 4

if you have the graph it is an eyeball problem
decreasing where it is going down, increasing where it is going up

Answer 5

btw it is an even function, symmetric wrt the y axis

Answer 6

what does wrt mean

Answer 7

with respect to

Answer 8

Okay.

Answer 9

Where should I start my interval at?

Answer 10

the numerator of your derivative is \(2x(1-x^4)\)
the denominator is a square, which is always positive
so what you need are the zeros of \(2x(1-x^4)\)

Answer 11

So when I find the zeros I will be able to find the intervals?

Answer 12

yes

Answer 13

Wait I thought that my numerator was a square

Answer 14

you can pretty much eyeball the zeros of \(2x(1-x^4)\) as \(-1, 0, 1\)

Answer 15

oh your numerator of the original function is a square, it is \(x^2\)
i was talking about the numerator of the derivative

Answer 16

oh okay. sorry I didn't know you were talking about the derivative. So my intervals of decrease are (-1,0) and my intervals of increase are (0,1)

Answer 17

you need i think to describe it over the whole real line, not just those parts
you are right as far as it goes, but you also need
increase over \((-\infty,-1)\)

Answer 18

and also decrease on \((1,\infty)\)

Answer 19

okay thank you!