# Determining the interval on which a function is increasing

• April 18th 2009, 02:04 PM
bosmith
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.
• April 18th 2009, 02:50 PM
Calculus26
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.
• April 18th 2009, 03:15 PM
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
$f(x)=x-x^{-2}$ is increasing when $x\in<-\infty,-1,26><1,\infty>$
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.
• April 18th 2009, 03:16 PM
bosmith
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.
• April 18th 2009, 03:35 PM
bosmith
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

Quote:

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
$f(x)=x-x^{-2}$ is increasing when $x\in<-\infty,-1,26><1,\infty>$
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.