 Hi and welcome to the session. Let us discuss the following question. Question says, find the maximum and minimum values if any of the following functions given by Hx equal to sin 2x plus 5. First of all, let us understand that if function f is defined on interval i, then if there exists c belonging to interval i such that fc is greater than equal to fx for all x belonging to interval i, then fc is called the maximum value of the function f in interval i and if fc is less than equal to fx all x belonging to i, fc is called minimum value of f in interval i. This is the key area to solve the given question. Let us now solve the solution. We are given function h given by Hx equal to sin 2x plus 5. Now we know sin function is less than equal to 1 and greater than equal to minus 1 for every x belonging to real numbers. So we can write sin 2x is less than equal to 1 and greater than equal to minus 1 for every x belonging to real numbers. Now this implies minus 1 plus 5 is less than equal to sin 2x plus 5 is less than equal to 1 plus 5 for every x belonging to R. Now this implies 4 is less than equal to sin 2x plus 5 less than equal to 6 for every x belonging to real numbers. Now we know sin 2x plus 5 is equal to Hx. So we can write it equal to 4 less than equal to Hx less than equal to 6. Now 4 is less than equal to Hx implies minimum value of function h is 4 and 6 is greater than equal to Hx implies 6 is the maximum value of function h. So this is our required answer. Minimum value of function h is equal to 4 and maximum value of function h is equal to 6. This completes the session. Hope you understood the session. Goodbye.