 Hello and welcome to the session. I am Deepika here. Let's discuss the question. Prove that the function given by fx is equal to x cube minus 3x square plus 3x minus 100 is increasing in r. So let's start the solution. Given fx is equal to x cube minus 3x square plus 3x minus 100 therefore f dash x is equal to 3x square minus 6x plus 3 and this is equal to let us take 3 common 3 into x square minus 2x plus 1 and this is again equal to 3 into x minus 1 whole square. Now f dash x which is equal to 3 into x minus 1 whole square is greater than equal to 0 for all x belongs to r being a perfect square hence given function is increasing in r. I hope the solution is clear to you. Bye and take care.