# Help with using the first derivative

## Homework Statement

Use the first derivative to determine where the graph of y = x/(x^2+1) is rising.

## The Attempt at a Solution

Ive figured the derivative to be (1-x^2) / (x^2+1)^2 and I know that the derivative > 0 will tell me where the graph is rising. Im just not sure how to figure that out. Do I need to simplify my derivative a bit more to make it work?

Mark44
Mentor
The denominator will always be positive, so all you need to do is determine where the numerator is positive, and where negative. Factor 1 - x^2 and see where it is zero, and where positive, and where negative.

"Factor 1 - x^2 and see where it is zero, and where positive, and where negative."

Im not sure I know what you mean here. Factored form it is (x-1)(x+1)

Its 0 when x = +-1 , positive for 0<x<1 negative for (-infin,0) (1,infin)?

lanedance
Homework Helper
i think you may have missed the effect of one of the factors...

you could say (1-x^2) is +ve:
when
1-x^2 >0
implying
x^2 < 1

HallsofIvy
Homework Helper
"Factor 1 - x^2 and see where it is zero, and where positive, and where negative."

Im not sure I know what you mean here. Factored form it is (x-1)(x+1)

Its 0 when x = +-1 , positive for 0<x<1 negative for (-infin,0) (1,infin)?
"Factored form" is NOT (x- 1)(x+ 1), it is (1- x)(1+ x).

And the graph of y= (1-x)(1+x)= 1- x2, is a parabola opening downward and so y is positive for x between -1 and 1. I don't where you got the "0" in "0< x< 1". Was that a typo?

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