 Hi, and welcome to the session. Let us discuss the following question. The question says, find the interval in which the function f given by fx equals to 4 sine x minus 2x minus x cos x divided by 2 plus cos x is first part is increasing, second part is decreasing. Let's now begin with the solution. We have to find the interval in which the function f, which is given by 4 sine x minus 2x minus x cos x divided by 2 plus cos x is increasing and decreasing. Now, fx can be written as sine x cos x divided by minus divided by 2 plus x divided by 2 plus x is equal to divided by 2 plus cos x minus. Question rule, derivative of 4 sine x divided by 2 plus cos x is equal to x cos x minus sine x is equal to therefore 0. When 0 is less than x is less than pi by 2, p pi by 2 is less than x. The given function f increases. 0 is less than x is less than pi by 2. 3 pi by 2 is less than the intervals in which the function is decreasing. So, let us check where the function is decreasing, when minus 1 is less than equal to cos x is less than equal to 1. Less than equal to 1 is greater than 0 being the fourth. So, this implies the function decreases. 2 is less than x is less than 3 pi by 2. So, we have found out that the given function f is increasing, when x lies between 0 and pi by 2 and also when x lies between 3 pi by 2 and 2 pi. Function f is decreasing when x lies between 3 pi by 2. So, this is our requirement on SOAPS. This completes the session by ending here.