Problem 59

Given information

Given that cubic function is in the form of    

Local maximum value  is 3  at  

Local minimum value is 0  at  

Step-by-step explanation

To find the cubic function, we need to calculate the values of . For this, we will find .

         .............(i)

               .............(ii)

Since the local maximum value is at , which means

and  

Substitute in equation (i) and (ii), we get

                              ............(1)

                                       ............(2)

Since the local minimum value is  at , which means

and  

Substitute  in equation (i) and (ii), we get

                                      ............(3)

                                        ............(4)