 Hi and welcome to the session. Let us discuss the following question. Question says, find the absolute maximum value and the absolute minimum value of the following functions in the given intervals. Function F is given by fx equal to x minus 1 whole square plus 3 where x belongs to closed interval minus 3, 1. First of all, let us understand that for finding absolute maximum or absolute minimum values of a function in a given closed interval, first of all we will find all critical points of function f in that interval. Find the value of function f at all the critical points and at the end points of the interval. Identify the maximum and minimum values of function f out of the values calculated in step 2. The maximum value will be the absolute maximum value of function f and the minimum value will be the absolute minimum value of function f. Okay idea to solve the given question. Now let us start the solution. We are given function f is given by fx equal to x minus 1 whole square plus 3 where x belongs to closed interval minus 3, 1. Now differentiating both sides with respect to x we get f dash x is equal to 2 multiplied by x minus 1 plus 0. We know derivative of x minus 1 whole square is 2 multiplied by x minus 1 and derivative of 3 is 0. So we get f dash x equal to 2 multiplied by x minus 1. To find critical points we will put f dash x equal to 0. This implies 2 multiplied by x minus 1 is equal to 0. Or simply we can say x minus 1 is equal to 0 dividing both sides by 2. We get x minus 1 is equal to 0. Now this implies x is equal to 1. Adding 1 on both sides we get x equal to 1. Now clearly we can see x equal to 1 is one of the end point of the closed interval minus 3, 1. So we will find value of function f at x equal to minus 3 and x equal to 1. So first of all let us find out value of function f at x equal to minus 3 f minus 3 is equal to minus 3 minus 1 whole square plus 3. Now this is equal to minus 4 square plus 3. We know minus 3 minus 1 is equal to minus 4. Now square of minus 4 is equal to 16. So we get f minus 3 is equal to 16 plus 3. Or we can simply write it as 19. Now let us find out value of the function f at x equal to 1. This is equal to 1 minus 1 whole square plus 3. We know 1 minus 1 is equal to 0. So we get f1 is equal to 3. Here we can see maximum value of function f is equal to 19. So we can say absolute maximum value is equal to 19 which occurs at x equal to minus 3 and minimum value of function f is equal to 3. So we can say absolute minimum value of function f is 3 which occurs at x equal to 1. So we can write absolute maximum value of function f is 19 that occurs at x equal to minus 3 and absolute minimum value of function f is 3 that occurs at x equal to 1. So this is our required answer. This completes the session. Hope you understood the session. Take care and keep smiling.