 Hi and welcome to the session I am Deepika here. Let's discuss the question, find the intervals in which the following function is strictly increasing or decreasing 10-6x-2x square. Now we know that a function f is strictly increasing in an open interval a, b if f-x is greater than 0 for each x belongs to a, b and f is strictly decreasing in an open interval a, b if f-x is less than 0 for each x belongs to an open interval a, b. This is a key idea behind our question. So let's start the solution given fx is equal to 10-6x-2x square. Therefore f-x is equal to minus 6-4x and this is equal to minus 2 into 3 plus 2x. Now f-x is equal to 0 implies x is equal to minus 3 by 2. Hence x is equal to minus 3 by 2 divides the real line into two disjoint intervals minus infinity to minus 3 by 2 and minus 3 by 2 to infinity. Now for x less than minus 3 by 2 this implies our f-x is equal to minus 2 into some negative number and this will be positive. This implies f-x is greater than 0. Hence f-x is strictly increasing for x less than minus 3 by 2. Now for x greater than minus 3 by 2 f-x is equal to minus 2 into some positive number and this will be negative number. This implies f-x is less than 0. Hence f-x is strictly decreasing for x greater than minus 3 by 2. Hence the answer for the above question is function is strictly decreasing for x greater than minus 3 by 2 and strictly increasing for x less than minus 3 by 2. This is the answer. I hope the question is clear to you. Bye and take care.