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Enter the function f(x), X₁ and X₂ long with values in the Average Rate of Change Calculator to determine f(x₁), f(x₂), f(x₁)-(x₂), (x₁-x₂), and the rate of change.
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Use this online average rate of change calculator to determine the average rate at which a function changes over a given interval. It measures how one quantity changes on average with respect to another. Let’s explore how to calculate the average rate of change using a formula.
The average rate of change measures how one quantity changes as another quantity changes. In other words, it is the total change in the output of a function divided by the total change in the input over a specific interval.
The standard formula is:
$$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} $$
Where:
To calculate the average rate of change, follow these steps:
Find the average rate of change of the function f(y) = 3y² + 5 over the interval [-1, 3].
Solution:
Step 1 – Identify the endpoints:
a = -1, b = 3
Step 2 – Evaluate the function at both endpoints:
$$ f(a) = f(-1) = 3(-1)^2 + 5 = 3 + 5 = 8 $$
$$ f(b) = f(3) = 3(3)^2 + 5 = 27 + 5 = 32 $$
Step 3 – Substitute into the formula:
$$ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} = \frac{32 - 8}{3 - (-1)} = \frac{24}{4} = 6 $$
From Wikipedia: Rate of Change .
From Brilliant: Average and Instantaneous Rate of Change .
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