Thread: 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.

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.

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
is increasing when
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.

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.

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
is increasing when
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.