 Hi, and welcome to the session. I am Deepika here. Let's discuss a question. Rule that the greatest integer function defined by fx is equal to x. 0 is less than x, x is less than 3, is not differentiable at x is equal to 1 and at x is equal to 2. So let's start the solution. x is equal to 1, limit x to 1 minus fx is equal to limit x to 1 minus, greatest integer function of x is equal to 0. Because from the definition of greatest integer function equal to, greater function of x is equal to 0 for 0 is less than equal to x, x is less than 1. Therefore limit x tends to 1 minus fx is equal to limit x tends to 1 minus, greatest integer function of x is equal to 0. Now limit x tends to 1 plus f of x is equal to limit x tends to 1 plus, greatest integer function of x this is equal to 1. Again from the definition of greatest integer function of x, this is equal to 1 for 1 is less than equal to x, x is less than 2. Therefore limit x tends to 1 plus fx is equal to limit x tends to 1 plus, greatest integer function of x is equal to 1. This implies limit x tends to 1 minus fx is not equal to limit x tends to 1 plus fx. Therefore, therefore limit x tends to 1 does not exist f is not continuous x is equal to 1. And since f is not continuous at x is equal to 1, not differentiable at x is equal to 1. One function is differentiable at x is equal to 2 or not. At x is equal to 2 limit x tends to 2 minus fx is equal to limit x tends to 2 minus, greatest integer function of x is equal to 1. Again this is by the definition of greatest integer function of x, because greatest integer function of x is equal to 1 for 1 is less than equal to x, x is less than equal to 2. And again limit x tends to 2 plus fx is equal to limit x tends to 2 plus, greatest integer function of x and this is equal to 2. This is again because by the definition of greatest integer function of x, greatest integer function of x is equal to 2 for 2 is less than equal to x, x is less than 3. Now limit 2 minus is not equal to limit x tends to 2 plus fx, therefore limit x tends to 2 does not exist, is not continuous x is equal to 2. Since f is not continuous at x is equal to 2, therefore f is not differentiable at x is equal to 2. This is equal to greatest integer function of x, 0 is less than x, x is less than 3, is not differentiable equal to 1, x is equal to 2, hence proved. I hope the question is clear to you, why and take care.