 Hi, and welcome to the session. Let us discuss the following question. The question says, verify Roll's theorem for the following function. fx is equal to x minus 1 into x minus 2 whole square on closed interval 1, 2. Now, we begin with the solution. We have to verify Roll's theorem for fx equals to x minus 1 into x minus 2 whole square on closed interval 1, 2. Now, since polynomial function is continuous and differentiable everywhere, being a polynomial function is continuous on closed interval 1, 2, and differentiable on open interval 1, 2. Two conditions of Roll's theorem are satisfied. We'll verify the third condition. So let's first find out f of a. Now, here a is equal to 1. So we have f of 1, and f of 1 is equal to 1 minus 1 into 1 minus 2 whole square, and this is equal to 0. Now, we will find f of b, where b is equal to 2. So we have f of 2, and f of 2 is equal to 2 minus 1 into 2 minus 2 whole square, and this is equal to 0. Clearly, f is equal to f of two conditions. Roll's theorem are satisfied, conclusion of Roll's theorem. That means now we have to show interval 1, 2, such that is equal to 0. This is equal to into x minus 2 whole square is equal to 2 whole square is equal to c minus 2 minus 4 into c minus 2 is equal to 0. This implies into c minus 2 is equal to 0, interval 1, 2.