 Hello and welcome to the session, I am Deepika here. Let's discuss the question, the intervals in which y is equal to x square into e raised to power minus x is increasing is a and open interval minus infinity to infinity, b and open interval minus 2 to 0, c 2 to infinity and d 0 to 2. So let's start the solution. Given y is equal to e raised to power minus x, therefore d y by dx is equal to, now we will use a product rule here into e raised to power minus x into minus 1 plus e raised to power minus x into 2x and this is equal to x square into e raised to power minus x plus 2x into e raised to power minus x and this is equal to since e raised to power minus x, let's take it common, we get 2 minus x and this is equal to e raised to power x into 2 minus x. Now x over, we know that e raised to power x is 1 plus x plus x square over 2 factorial plus so on into 2 minus x and this is equal to, now this is some positive quantity into 2 minus x. Now for an increasing function, now for an increasing function is greater than 0, this implies c into 2 minus x should be greater than 0 because denominator is already positive here. So this implies either this is greater than 0 and 2 minus x is greater than 0 or x is less than 0 and 2 minus x is less than 0. Now if x is greater than 0 is greater than 0, this implies x is greater than 0 and less than 2. So this is the interval 0, open interval 0 to 2, function increases in open interval 0 to 2 that is x is greater than 0 and x is less than 2. Now if x is less than 0 and 2 minus x is less than 0 implies 2 is less than x, that is x is greater than 2, that is not possible, that is x is greater than 2 but x is less than 0 so this is not possible. So we will not take the case, hence the answer for the above question is d that is in this interval, in the interval 0 to 2 the function is increasing. I hope the question is clear so you may and take care.