Write a difference quotient that best approximates the instantaneous rate of change of g at x=0 Please show how you got your answer

We can define the average rate of change of a function f(x) in an interval [a, b] as:

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:

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:

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step-by-step explanation: