How do I find the instantaneous ROC at x=1.5

What does ROC stand for? Isn't there more information that goes with this question?

Is ROC the Region of Convergence? of what?

Just curious.

To find the instantaneous rate of change (ROC) at x = 1.5, you'll need to know the function that represents the relationship between two variables. Let's assume you have a function denoted as f(x).

To find the instantaneous ROC at x = 1.5, you can follow the steps below:

1. First, calculate the difference between the function values at two points, where the first point is very close to x = 1.5 and the second point is x = 1.5. Let's denote these points as (x1, f(x1)) and (x2, f(x2)), respectively. In this case, we can choose x1 = 1.5 - h and x2 = 1.5, where h is a small positive number.

2. Evaluate f(x1) and f(x2) by substituting x1 and x2 into the function f(x). This will give you the respective function values, denoted as f(x1) and f(x2).

3. Calculate the difference in function values: Δy = f(x2) - f(x1).

4. Calculate the difference in x-values: Δx = x2 - x1, which in this case is 1.5 - (1.5 - h) = h.

5. Finally, calculate the instantaneous ROC by dividing Δy by Δx: ROC = Δy/Δx.

By taking the value of h closer and closer to zero, the result will approach the true instantaneous ROC at x = 1.5.