Understanding the Instantaneous Rate of Change | Calculating and Interpreting Derivatives

Instantenous Rate of Change

The instantaneous rate of change, also known as the derivative, measures the rate at which a function is changing at a specific point or instant

The instantaneous rate of change, also known as the derivative, measures the rate at which a function is changing at a specific point or instant. It gives us information about how fast or slow a function is changing at that particular point.

To calculate the instantaneous rate of change, we use calculus and the concept of the derivative. The derivative of a function f(x) with respect to x is denoted as f'(x) or dy/dx. It represents the slope of the tangent line to the graph of the function at a given point.

To find the instantaneous rate of change at a specific point x=a, we can find the derivative of the function with respect to x, and then substitute x=a into the derivative expression.

For example, if we have a function f(x) = 3x^2 – 2x + 1 and we want to calculate the instantaneous rate of change at x=2, we start by finding the derivative of f(x). Taking the derivative, we get f'(x) = 6x – 2.

Then, we substitute x=2 into the derivative expression: f'(2) = 6(2) – 2 = 10.

The instantaneous rate of change at x=2 is 10. This means that at the point x=2, the function is changing at a rate of 10 units for every unit of change in the x-coordinate.

In summary, the instantaneous rate of change represents how fast a function is changing at a specific point. It is calculated using the derivative and gives us valuable information about the behavior of functions.

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