Instantaneous rate of change (IR. c)
The instantaneous rate of change (IRC) is a concept in calculus that measures how quickly a function is changing at a specific point on its graph
The instantaneous rate of change (IRC) is a concept in calculus that measures how quickly a function is changing at a specific point on its graph. It is also referred to as the derivative of the function at that particular point.
To understand IRC, let’s consider a function f(x) that represents the height of an object at different points in time. The IRC at a particular time t measures the rate at which the height of the object is changing exactly at that moment.
Mathematically, we can calculate the IRC by taking the derivative of the function f(x) with respect to x and then evaluating the derivative at the specific value of x or t.
Here is the general formula for IRC:
IRC = lim(h->0) [f(x+h) – f(x)] / h
In this formula, h represents a very small change in x, approaching zero. By calculating the difference in function values (f(x+h) – f(x)) divided by the small change in x (h), we can approximate the rate of change of the function at a specific point.
For example, let’s say we have a function f(x) = 2x^2 – 3x + 1, and we want to find the IRC at x = 2. We can start by finding the derivative of f(x) using calculus techniques, which in this case is f'(x) = 4x – 3.
Next, we plug in the value of x = 2 into the derivative:
f'(2) = 4(2) – 3 = 5
Therefore, the IRC of f(x) at x = 2 is 5. This means that at x = 2, the function is changing at a rate of 5 units per unit of x.
It is important to note that IRC provides information about the rate of change at a specific point, while the derivative represents the rate of change at any point on the graph of the function. IRC is useful in various fields such as physics, economics, and engineering, where it helps to analyze the behavior and trends of functions at specific moments in time or specific values of variables.
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