 Hi, and welcome to the session. I am Deepika here. Let's discuss the question. Find the intervals in which the function f given by fx is equal to 2x square minus 3x is a strictly increasing b strictly decreasing. Let us first understand the definition of strictly increasing and strictly decreasing. The function is strictly increasing or decreasing an interval where its derivative is positive or negative. That is, a function is strictly increasing on an open interval where its derivative is positive and a function is strictly decreasing on an open interval where its derivative is negative. So, this is a key idea behind our question. We will take the help of this key idea to solve up our question. So, let's start the solution. Given fx is equal to 2x square minus 3x, therefore f dash x is equal to 4x minus 3. Now, f dash x is equal to 0 implies x is equal to 3 by 4. Now, the point x is equal to 3 by 4 divides the real line into two disjoint intervals minus infinity to 3 by 4 and 3 by 4 to infinity. Now, part a, a function is strictly increasing f dash x is greater than 0. This implies 4x minus 3 is greater than 0 and this implies x is greater than 3 by 4. It means f is strictly increasing in 3 by 4 to infinity in 3 by 4, open interval 3 by 4 to infinity. Hence, the answer for this part is open interval 3 by 4 to infinity. I hope this part is clear to you. Now, part b, a function is strictly decreasing if its derivative is negative. f dash x is less than 0. This implies 4x minus 3 is less than 0 and this implies x is less than 3 by 4. Hence, in an open interval minus infinity to 3 by 4, f is strictly decreasing. That is, f is strictly decreasing in minus infinity to 3 by 4. Hence, the answer for this part is open interval minus infinity to 3 by 4. I hope the question is clear to you. Bye and take care.