Answer:
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
Explanation: