 Hi and welcome to the session. I am Deepika here. Let's discuss a question. If fx is equal to mod x cube Show that f double dash x exist for all real x and find it. So let's start the solution Now according to the definition of mod x Our given function is fx is equal to mod x cube. So according to the definition When x is greater than equal to 0 or fx is equal to x cube. So f dash x is equal to 3x cube and f double dash x is equal to 6x which exists For all real values of x Again when x is less than 0 fx is equal to minus x cube So therefore f dash x is equal to minus 3x square and f double dash x is equal to minus 6x Which also exists For all real values of x We have shown that if fx is equal to mod x cube f double dash exist for all real values of x and f double dash x is equal to 6x if x is greater than equal to 0 and it is minus 6x if x is Less than 0. So this is our answer I hope the question is clear to you. Bye and have a nice day