Note that, in general,
g(1 h)!=g(1) h
. ii) Now, for the same function
g
defined abowe, evaluate the so-called average rates of change on the intervals
(1,2),(1,1.5),(1,1.1),[1,1.01],[1,1.001]
, sas well sas the average rate of change of
g
over the more general interval
1,x
, as follows: a)
(g(2)-g(1))/(2-1)=
b)
(g(1.5)-g(1))/(1.5-1)=
c)
(g(1.1)-g(1))/(1.1-1)=
d)
(g(1.01)-g(1))/(1.01-1)=
1