 Hi and welcome to the session. I am Shashi and I am going to help you with 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 sin x plus cos x, where x belongs to close interval 0, i. First of all let us understand that to find absolute maximum or absolute minimum value of a function in a given closed interval. First of all we will find all critical points of function f. Now we will find value of function f at all critical points and at the end points of the interval. Now we will identify the maximum and minimum values of function f out of all these values calculated in this step. 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. This is the key idea to solve the given question. Now let us start the solution. We are given fx is equal to sin x plus cos x, where x belongs to close interval 0, i. Now to find critical points first of all we will find f dash x differentiating both sides with respect to x we get f dash x equal to cos x minus sin x. Critical points we will put f dash x equal to 0. Now we get cos x minus sin x equal to 0. This implies cos x is equal to sin x. Adding sin x on both sides we get cos x is equal to sin x. Now dividing both sides by cos x we get 1 is equal to sin x upon cos x. Now we know sin x upon cos x is equal to tan x. So we get 1 is equal to tan x or we can write tan x equal to 1. Now we know tan pi upon 4 is equal to 1. So we get x is equal to pi upon 4. Clearly we can see pi upon 4 lies in the close interval 0 pi. So we get x equal to pi upon 4. Now this completes the first step of the key idea. Now we will find value of f and x equal to pi upon 4 and x equal to 0 and then x equal to pi. So first of all we will find f0 which is equal to sin 0 plus cos 0 which is equal to 0 plus 1 or we can simply write it as 1. So we get f0 is equal to 1. Now let us find out f pi upon 4. This is equal to sin pi upon 4 plus cos pi upon 4. We know sin pi upon 4 is equal to 1 upon root 2 and cos pi upon 4 is also equal to 1 upon root 2. So it is equal to 2 upon root 2. Now rationalizing we get f pi upon 4 equal to root 2. Now we will find out value of f at x equal to pi. So f pi is equal to sin pi plus cos pi. Now we know sin pi is equal to 0 and cos pi is equal to minus 1. So we can write it equal to 0 plus minus 1. Now on simplifying we get f pi equal to 0 minus 1 or we can simply write it as minus 1. Now this completes the second step of the key idea. Now we will identify the maximum and minimum value of function f. Minimum value is equal to minus 1 and maximum value is equal to root 2. So now we can write absolute minimum value of function f in closed interval 0 comma pi is minus 1 which occurs at x equal to pi. Now absolute maximum value of function f in closed interval 0 comma pi is root 2 up to get x equal to pi upon 4. Then we can see absolute maximum value of function f is root 2 which occurs at x equal to pi upon 4. So this is our required answer. This completes the session. Hope you understand the session. Take care and have a nice day.