 Hi and how are you all today? The question says find the intervals in which the function f given by fx is equal to 4x squared plus 1 upon x raised to the power 2 is increasing or decreasing. So here we are given the function as 4x squared plus 1 upon x raised to the power 2. Let us find out first derivative that will be x squared into 8x that is the derivative of the numerator minus numerator into derivative of the denominator whole upon denominator whole square. So it is further equal to x cube minus x cube minus upon x raised to the power 4 that is further equal to minus 2x upon x raised to the power 4 that is minus 2 upon x raised to the power 3. Now for increasing, decreasing function we put f dash x equal to 0. So in doing so we have minus 2 upon x cube equal to 0 this implies x is equal to, so therefore intervals are minus infinity to 0, 0 to infinity. Now in interval minus infinity to 0 we have f dash x positive and in interval 0 to infinity we have f dash x equal to negative. So thus we can write down that function is increasing in the interval minus infinity to 0, decreasing in interval 0 to infinity. Right, so this completes the session. Hope you understood the whole concept well. Enjoy it. Bye for now.