The discussion revolves around finding the intervals of increase or decrease for the function f(x) = (3/(x^2 + 11)) - 1. Participants are examining the first derivative, f'(x), and its implications for the behavior of the function.
The discussion is ongoing, with participants exploring the implications of the first derivative and questioning the signs of the numerator in different intervals. Guidance has been offered regarding the positivity of the denominator and its relevance to the analysis of the function's behavior.
There is a noted typo in the original derivative calculation, and participants are addressing the implications of this error. Additionally, there is confusion regarding the domain of the function and the interpretation of negative values in the context of the problem.
ifi2world said: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.
Pranav-Arora said: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.
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?ifi2world said:yes.. sorry for typo error.
so what should i do next to get the interval?
but how to square root the -11? isn't that impossible or does it have another formula?
Pranav-Arora said: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?