 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. The question says, find the maximum and minimum values if any of the following functions given by fx equal to 9x square plus 12x plus 2. First of all let us understand that if function f is defined on interval i then if there exists a point c belonging to interval i such that fc is greater than equal to fx for all x belonging to interval i then the number fc is the maximum value of function f in interval i and if fc is less than equal to fx for all x belonging to interval i then fc is called minimum value of function f in interval i. This is the key idea to solve the given question. Let us now start the solution. We are given fx is equal to 9x square plus 12x plus 2. Now adding and subtracting 4 x expression we get fx equal to minus square plus 12x plus 4 minus 4 plus 2. Now this is equal to 3x plus 2 whole square. So we can write 3x plus 2 whole square minus 2. We know minus 4 plus 2 is equal to minus 2. So we can write fx is equal to 3x plus 2 whole square minus 2. Now we know fx square cannot be negative so we can write 3x plus 2 whole square is greater than equal to 0. Now subtracting 2 from both sides we get 3x plus 2 whole square minus 2 is greater than equal to 0 minus 2. This implies 3x plus 2 whole square minus 2 is greater than equal to minus 2. Now this expression is equal to fx. So we can write fx is greater than equal to minus 2. Now clearly we can see fx is greater than equal to fc where fc is equal to minus 2. So minus 2 is the minimum value of function f given by 9x square plus 12x plus 2. So our required answer is minus 2. This completes the session. Hope you understood the session. Take care and bye.