# Thread: Determining the interval on which a function is increasing

1. ## Determining the interval on which a function is increasing

I need to determine the interval on whhich f(x) = x - x^(-2) is increasing. I think I should first get the derivative: F' = 1 - (-2x^-3)
= 1 + 2x^-3
= 1 + 2/x^3

I hope I wrote the function = x minus x to the minus 2. I derived 1 + 2 divided by x cubed. Even if I got the derivative right, I do not know how to use this derivative to determine when the function is increasing. Do I make the derivative greater than zero? Please help.

2. Set the derivative equal to 0 this diveides the x axis inot regions where f ' is always positive or always negative

then use test points in these regions to determine which.

3. if you have a graphic calculator you can simply add the formula, I have casio fx-970 and I have a program called graphic function witch can write functions and analyze them.

My answer from my calculator was
$\displaystyle f(x)=x-x^{-2}$ is increasing when $\displaystyle x\in<-\infty,-1,26><1,\infty>$
The space between is where the function is decreasing

And then you have to do the same for the derivative and maybe the second derivative. Hope this helps something.

4. ## Determining increasing and decreasing intervals of a function

Senior Member/ Calculus 26. Thatnk you so much for showing me how to determine the increasing interval. I really needed the teaching. I wish you all the best, and will no doubt be asking more questions. Thanks.

5. ## Increasing and decreasing intervals

Thanks hlolli. I purchased a TI-89 Titanium about a month ago. I haven't fully learned how to use it just yet. I am working at it as so my Calculus I course, a little slowly. Thanks

Originally Posted by hlolli
if you have a graphic calculator you can simply add the formula, I have casio fx-970 and I have a program called graphic function witch can write functions and analyze them.

My answer from my calculator was
$\displaystyle f(x)=x-x^{-2}$ is increasing when $\displaystyle x\in<-\infty,-1,26><1,\infty>$
The space between is where the function is decreasing

And then you have to do the same for the derivative and maybe the second derivative. Hope this helps something.