Intervals of increase and decrease

[ifi2world]

Homework Statement

find the intervals of increase or decrease of the function f(x)= (3/(x^2+11)-1

i already find the 1st derivative f'(x)= -6x/ (x^2 +11). After that i didnt know how to proceed to find the interval. I need help for the solutions.

 

[Sourabh N]

How does the first derivative behave in the interval of increase?

 

[Saitama]

Homework Statement

find the intervals of increase or decrease of the function f(x)= (3/(x^2+11)-1

i already find the 1st derivative f'(x)= -6x/ (x^2 +11). After that i didnt know how to proceed to find the interval. I need help for the solutions.

Do you mean
f(x)=\frac{3}{x^2+11}-1
If so, check the f'(x) you have calculated. The denominator should be squared.

 

[ifi2world]

Do you mean
f(x)=\frac{3}{x^2+11}-1
If so, check the f'(x) you have calculated. The denominator should be squared.

yes.. sorry for typo error.
so what should i do next to get the interval?
i need to find x after i did the 1st derivative but how to square root the -11? isn't that impossible or does it have another formula?

 

[Saitama]

yes.. sorry for typo error.
so what should i do next to get the interval?

If you examine the derivative, the denominator is squared and is always positive, so we don't really need to worry about that. Now see the numerator, what is the sign of the expression when x<0, what it is when x>0?

but how to square root the -11? isn't that impossible or does it have another formula?

Not really following what you are asking here.

 

[ifi2world]

If you examine the derivative, the denominator is squared and is always positive, so we don't really need to worry about that. Now see the numerator, what is the sign of the expression when x<0, what it is when x>0?

the sign is + for x<0 & - for x>0...so next is i need to find the domain for the function for the interval value...right?