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
[tex]f(x)=\frac{3}{x^2+11}-1[/tex]
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?
Intervals of increase and decrease refer to the portions of a graph or function where the values are increasing or decreasing, respectively. These intervals can be identified by analyzing the slope of the graph or the sign of the derivative of the function.
To find the intervals of increase and decrease, you can first find the derivative of the function. Then, set the derivative equal to zero to find the critical points of the function. The intervals between these critical points are the intervals of increase and decrease.
Intervals of increase and decrease provide important information about the behavior of a function. They can help identify the maximum and minimum values of the function, as well as the direction of its change.
Intervals of increase and decrease are closely related to the concavity of a function. A function is concave up (or increasing) in an interval if the derivative is positive in that interval. Similarly, a function is concave down (or decreasing) in an interval if the derivative is negative in that interval.
Yes, a function can have multiple intervals of increase and decrease. This can occur if the function has multiple critical points or if the function changes direction more than once. It is important to carefully analyze the function to identify all of its intervals of increase and decrease.