What is the difference quotient of 10/(x+4)?

Question

 I need help on this one!

Answer 1

The difference quotient for f(x) is [f(x+h)-f(x)]/h

 

So, for the given function, we get [10/(x+h+4) - 10/(x+4)]/h

 

          = [10(x+4)-10(x+h+4)]/[(x+4)(x+h+4)]

            -----------------------------------------------

                                     h

 

          = -10h/[h(x+4)(x+h+4)]

 

          = -10/[(x+4)(x+h+4)]

 

Note:  If we take the limit of the above expression as h approaches 0             (replace h by 0), we get -10/(x+4)², which is the derivative of               10/(x+4).