Math

Average Rate of Change Calculator

Find the average rate of change of a function between two points.

Calculated Output

Average rate of change 2

Formula: rate = (f(x₂) − f(x₁)) ÷ (x₂ − x₁)

Step-by-Step Breakdown

1. Values used:

2. x₁ = 1

3. f(x₁) = 3

4. x₂ = 5

5. f(x₂) = 11

7. Average rate of change = 2

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The math behind it

It is the change in output divided by the change in input: (f(x₂) − f(x₁)) ÷ (x₂ − x₁).

From (1, 3) to (5, 11) → (11 − 3) ÷ (5 − 1) = 2.

Is this the same as slope?

Yes — over an interval it equals the slope of the secant line.