 Hi, and welcome to the session. I am Deepika here. Let's discuss a question. Find the intervals in which the following function is strictly increasing or decreasing. Minus 2xq minus 9xq minus 12x plus 1. Let us first understand when a function is strictly increasing or decreasing. Let F be continuous on closed interval AB, differentiable on an open interval AB. Then F is strictly increasing open interval AB. If 10x is greater than 0, for each x belongs to an open interval AB and F is strictly decreasing if its derivative is negative. If F dash x is less than 0, for each x belongs to AB. So this is the key idea behind our question. Let us take the help of this key idea to solve the above questions. Given Fx is equal to minus 2xq minus 9x square minus 12x plus 1. Therefore, F dash x is equal to minus 6x square minus 18x minus 12 and this is equal to Let us take minus 6 comma x square plus 3x plus 2. Now factorize x square plus 3x plus 2. This is equal to minus 6x square plus 2x plus x plus 2. And this is equal to minus 6x into x plus 2 plus 1x plus 2. And this is equal to minus 6x plus 1x plus 2. Now F dash x is equal to 0 gives x is equal to minus 1 or x is equal to minus 2. Now the points x is equal to minus 1 and x is equal to minus 2 divides the real line into 3 disjoint intervals minus infinity to minus 2 minus 2 to minus 1 and minus 1 to infinity. Now let us consider these intervals one by one. We will see the derivative of our given function is positive or negative. If it is negative, then our function is strictly decreasing in that interval. And if it is positive, then our function is strictly increasing in that interval. Now for x less than minus 2 F dash x is negative because in the interval minus infinity to minus 2 both x plus 1 and x plus 2 are negative and their product is positive. But when they are multiplied by minus number again we will get F dash x is equal to minus number. Hence F dash x is less than 0 for x less than minus 2. Therefore F is strictly decreasing in this interval in minus infinity to minus 2. For minus 2 less than x x less than minus 1 F dash x is bigger than 0. Therefore F is strictly increasing in this interval in an open interval minus 2 to minus 1. For x greater than minus 1 F dash x is again less than 0. Therefore F is strictly decreasing in this interval. Hence the answer for the above question is function is strictly increasing for minus 2 is less than x, x is less than minus 1 and strictly decreasing for x less than minus 2 and x greater than minus 1. Hence this is the answer for the above question. I hope the question is clear to you. Bye and take care.