Average Rate of Change Formula

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Average rate of change formula is A(x) = f(b) - f(a)/ (b-a). Here f(x) is the given function with the independent variable, x. A(x) is the average rate of change of the function. The values a, b are the two input values and f(b) and f(a) are their corresponding function values for which the average rate of change needs to be calculated.
 
Example 1: Find the average rate of change in the values for the function, f(x) = x2+ 1 from 3 to 1
Given the function f(x) = x2 + 1.
Now, average rate of change is to be calculated for values from 3 to 1.
First, f(3) = 32 + 1 = 9+ 1 = 10 
Then, f(1) = 12 + 1 = 1+ 1 = 2 
Change in values between 3 to 1 is f(3) - f(1) = 10 - 2 =8
Average rate of change = 8/ (3-1) = 8/2 = 4
 
Example 2: Find the average rate of change in the values for the function, f(x) = x-2 from 10 to 6.
Given the function f(x) = x - 2.
Now, average rate of change is to be calculated for values from 10 to 6.
First, f(10) = 10 - 2 = 8
Then, f(6) = 6 - 2 = 4
Change in values between 10 to 6 is f(10) - f(6) = 8 - 4 =4
Average rate of change = 4/ (10-6) = 4/4 = 1

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