Find the average rate of change of the function on the interval specified for real number h.

Question

Find the average rate of change of the function on the interval specified for real number h.

r(t) = 4t3
on
[2, 2 + h]

Answer 1

Use the formula

 

rate = f(t + h) - f(t)

          ___________

                   h

 

 

       = 4(2 + h)³ - 4(2)³

          _____________

                      h

 

 

 

       = 4(4 + 4h + h²)(2 + h) - 32

           _______________________

                           h

 

 

      = (16 + 16h + 4h²)(2 + h) - 32

         __________________________

                            h

 

 

     =  32 + 32h + 8h² + 16h + 16h² + 4h³ - 32

         ___________________________________

                                     h

 

 

     =  48h + 24h² + 4h³

         ______________

                    h

 

     = 48 + 24h + 4h²