Calculus Question: Determining intervals

[Put a quark in it]

Greetings,

I have a question about determining intervals of increase or decrease on a given function. For example...

f(x) = (X-1)/(X^2+3)

The next step is to get the derivative, which is...

f'(x) = ((X^2 + 3) - 2X^2 + 2X))/(X^2+3)^2

Then, you set that equal to zero and solve for X, and f'(x) = 0 at -1 and 3. So now, my interval is -1 to 3. According to my textbook, I should then choose a numer (c) on the numberline, plug it into f'(c'), and if it is less than zero than it is decreasing, and if is greater than zero it is increasing. However, according to the answer key for this particular problem, the interval is descreasing at x < -1 and x > 3, and increasing at -1 < x < 3. What am I not understanding? Thanks for any help.

Edit: I show that it is increasing when x < -1, increasing when x is between -1 and 3, and increasing when x > 3

Edit^2: Nevermind... I tried to simplify f'(x) into (-X^2 + 2X + 3)/(X^2+3)^2 and that's what was given me problems.

 

[lippyka]

What you are not understanding is that the derivative of your function tells you what is happening to the function in the intervals around each point. For example, when x < -1, the derivative is negative, which means the function is decreasing in that interval. Similarly, when x is between -1 and 3, the derivative is positive, so the function is increasing in that interval. Finally, when x > 3, the derivative is negative again, so the function is decreasing in that interval.