 Hi and welcome to the session, let's work out the following question. The question says, find the intervals in which the function fx equals to 2xq minus 15x squared plus 36x plus 1 is strictly increasing or decreasing. Also find the points on which the tangents are parallel to x axis. So let's start with the solution to this question. Let fx be equal to 2xq minus 15x squared plus 36x plus 1. Therefore f dash x will be equal to 6x squared minus 30x plus 36. This is equal to 6 into x minus 2 into x minus 3. This we call 1. Now we have to determine for what value of x is f dash x greater than 0. We see that f dash x is greater than 0 or we can say it is greater than 0 if x minus 2 and x minus 3 simultaneously positive or negative. That is f dash x is greater than 0. 6 into x minus 2 into x minus 3 is greater than 0. Since this is greater than 0, so x minus 2 into x minus 3 is greater than 0 or x minus 2 is greater than 0. x minus 3 greater than 0 or x minus 2 less than 0 and x minus 3 less than 0 or we can say that if x is greater than 2 and x is greater than 3 or x is less than 2 and x is less than 3. Therefore from these two statements we can say that x is greater than 3 or x is less than 2. Therefore function we have to determine for what value of x is f dash x less than 0. That is it is decreasing. So we can say 6 into x minus 2 into x minus 3 is less than 0. Therefore either x minus 2 is greater than 0, minus 3 is greater than 0. We can say that x is greater than 2. Given function is decreasing for 2 less than x less than 3 is equal to 0 minus 15 x squared equals to 2 becomes y equals to 2 into 2 cubed minus 15 into 2 plus 36 into 2 plus 1. This is further equal to 16 minus 60 plus 72 plus 1 which is equal to 29 and for x equals to 3 y becomes 2 into 3 cubed 3 minus here we have 15 into 3 squared plus 36 into 3 plus 1. This is equal to 54 minus 135 plus 108 plus 1 and this is equal to 28. Therefore the points are 29 or 328. This is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.