 Hi and welcome to the session. Let us discuss following question. Question says, a grammar if roles theorem is applicable to any of the following functions. Can you say something about the converse of roles theorem from these example? Second part is fx is equal to greatest integer of x for x belonging to closed integral minus 22. First of all let us understand what is roles theorem. If we are given a function f from closed interval ab to r and function is continuous on closed interval ab, function f is differentiable on open interval ab, f a is equal to f b. Then there exists some c belonging to open interval ab such that f dash c is equal to 0. This is the key idea to solve the given question. Let us now start with the solution. We are given fx is equal to greatest integer of x for x belonging to closed interval minus 22. Now we know function f given by fx is equal to greatest integer of x is not continuous at all integer points. So we can write fx is equal to greatest integer of x is not continuous for x belonging to closed interval minus 22. So the given function does not satisfy the first condition of roles theorem. So roles theorem is not applicable here. Now let us discuss about converse of roles theorem. Converse of roles theorem states that if we are given a function f from closed interval ab to r such that this function is continuous on closed interval ab and differentiable on open interval ab and c belongs to open interval ab such that f dash c is equal to 0. Then f a is equal to f b. Now clearly we can see first condition given in the converse of roles theorem is not satisfied by the given function. So we can say converse of roles theorem is not applicable to the given function. So we can write converse of roles theorem applicable to the given function. Now clearly we can see if roles theorem is not applicable to the given function then converse of roles theorem is also not applicable to it. So this completes the session. Hope you understood the session. Take care and have a nice day.