We can define the average rate of change of a function f(x) in an interval [a, b] as:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Particularly, if we want to find an approximation of the rate of change for a particular value x', we can choose:
a < x' < b
Such that a and b are really close to x'.
Then if we want to find the instantaneous rate of change of g at x = 0, we need to find values of a and b really close to zero.
Looking at the table, we can choose:
a = -0.001
b = 0.001
(are the two closer ones to zero)
Then the rate of change can be written as:
[tex]f(x) = \frac{g(0.001) - g(-0.001)}{0.001 - (-0.001)} = \frac{2.001 - 1.999}{0.002} = 1[/tex]
From that, we can conclude that a good approximation of the instantaneous rate of change is 1.
If you want to learn more, you can read:
https://brainly.com/question/18904995
