# 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?

## Answers and Replies

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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