Rate of change x=3 x=5

The average rate of change for g(x) is      { g(x+h)-g(x) }/h

In our case,

                             { log(5+1) - log(3+1) }/(5-3) =    (.778-.602)/2 = .088

Compare it to the derivative of log(x+1) for the values: the derivative is D = (1/ln10)(1/(x+1))

at x = 3      D = .1086

at x = 4      D =  .0869

at x = 5      D = .0724

Take the average of D over the interval and you get .0893  and very close to the midpoint of the x values

Step-by-step explanation: