Average Rate of Change Calculator

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Average rate of change is therate at which the function value is changing with respect to the change in the ‘x’ value. Average rate of change for any given function or curve is also called the slope at the given points. Average rate of change calculator is the tool which can easily find the slope or the average rate of change.

Example 1: Find the average rate of change (or slope) of the function, f(x) = 3x – 5 when the ‘x’ value changes from -3 to 1.

Average rate of change = [f(b) – f(a)] / (b-a)

’x’ is changing from -3 to 1  a = -3 and b = 1

f(-3) = (3*-3)–5 = -9 – 5 = -14

f(1) = (3*1) – 5 = 3 – 5 = -2

Average rate of change = [-2 – (-14)] / [(1 – (-3)]  (-2 +14)/ (1 + 3)  12/4 = 3

Average rate of change = 3

Example 2: Find the average rate of change (or slope) of the function, f(x) = 2x + 4 when the ‘x’ value changes from 0 to 3.

Average rate of change = [f(b) – f(a)] / (b-a)

’x’ is changing from 0 to 3 a = 0 and b = 3

f(0) = (2*0)+4 = 0+4 = 4

f(3) = (2*3)+4 = 6+4 = 10

Average rate of change = [f(3) – f(0)] / (3 – 0)

(10–4) / (3-0) = 6/3 = 2

Average rate of change = 2