 Hello friends and how are you all today? The question says, find the intervals in which the function fx equal to xq minus 12x squared plus 36x plus 17 is a increasing, b decreasing. So here the function which is given to us is xq minus 12x squared plus 36x plus 17. Let us first find out its derivative. So its first derivative will be 3x squared minus 24x plus 36, right? And I am taking 3 common, we are left with x squared minus 8x plus 12 for this function to be increasing. The first derivative should be greater than 0 for this function to be decreasing. This first derivative should be less than 0. So we have 3x squared minus 8x plus 12 greater than 0. This implies x squared minus 8x plus 12 is greater than 0. This further implies in splitting the middle term we have 2 factors that is x minus 2 and x minus 6 that is greater than 0. This implies that greater than, so this implies in 2 intervals it is greater that is from minus infinity to 2, 6 to infinity. x belongs to, we will be finding it for the decreasing function also. So we have 3 bracket x squared minus 8x plus 12 less than 0. This implies x squared minus 8x plus 12 is less than 0. This implies x minus 2, x minus 6 is less than 0. So this implies this is greater than 2 or less than, this function is increasing on the interval minus infinity to 2, infinity and b. It's decreasing on the interval 2 to 6, right? So this is the required answer to the given question. Hope you understood it well and enjoyed it also. Have a nice day ahead.