ASK A QUESTION How do you find the rate of change of f(x)= 3/(x+1) on the interval [x,x+h} ? Please help!!! Thank you!!

Question

f(x) is 3 over x+1 I just can't figure out how to do a fraction bar! Thank you!!

Answer 1

You will use the difference quotient.

 

f(x + h) - f(x)

_____________

           h

 

 

 

       3                               3

  __________      -      _________ 

   x + h + 1                    x + 1

 

__________________________________          =

                           h

 

 

 

 

        3(x + 1)  -  3(x + h + 1)

       _____________________

              (x + h + 1)(x + 1)

_____________________________________   =

                        h

 

 

 

 

      3x + 3 - 3x - 3h - 3

   _______________________

     x² + xh + x + x + h + 1

___________________________        =

                   h

 

 

 

                     -3h

        _____________________   

          x² + xh + 2x + h + 1

____________________________        =

                         h                 

 

 

 

              -3

 ___________________

 

    x² + xh + 2x + h + 1