 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 fx is equal to minus of x minus 1 whole square plus 10. First of all let us understand that if function f is defined on interval i then if there exists c in the interval i such that fc is greater than equal to fx for all x belonging to interval i then fc is known as maximum value of function s in interval i and if there exists c in interval i such that fc is less than equal to fx for all x belonging to interval i then fc is called the minimum value of function x in interval i. This is the key idea to solve the given question. Let us now start the solution. We have given fx is equal to minus x minus 1 whole square plus 10. Now we know that fx square cannot be negative so we can write x minus 1 whole square is greater than equal to 0. Now this implies minus of x minus 1 whole square is less than equal to 0. Now adding 10 on both sides we get minus x minus 1 whole square plus 10 is less than equal to 10. Now we know this expression is equal to fx so we can write fx is less than equal to 10. Now clearly we can see here fc is equal to 10 and it is greater than equal to fx so the number fc that is 10 is the maximum value of the function f so we can write 10 is the maximum value of function f by fx equal to minus x minus 1 whole square plus 10. So our required answer is maximum value of the function f is 10. This completes the session. Hope you understood the session. Goodbye.