 Hi and welcome to the session. Let us discuss following question. Question says, exam in the applicability of mean value theorem for the given functions. First part is, fx is equal to greatest integer of x for x belonging to closed interval 5 line. First of all let us understand what is mean value theorem. Mean value theorem states that if we are given a function f from closed interval ab to r and this function is continuous on closed interval ab and differentiable on open interval ab when there exists some c belonging to open interval ab such that f dash c is equal to fv minus f a upon b minus a. We will use this theorem as key idea to solve the given question. Now let us start with the solution. We are given fx is equal to greatest integer of x for x belonging to closed interval 5 line. Now we know given function is not continuous at all integer points. So we can say fx is equal to greatest integer of x is not continuous for x belonging to closed interval 5 line. So clearly we can see given function does not satisfy first condition of mean value theorem. So we can write mean value theorem is not applicable to the given function. So this is our required answer. This completes the session. Hope you understood the session. Take care and have a nice day.