Average Rate of Change

Q:  Find the average rate of change of y if x changes from 2 to 5 in the function y = x² + 2x


A:  So, the average rate of change can be measured by (y2 – y1)/(x2 – x1)

So far, we have x1 = 2 and  x2 = 5

(the order of which is x1 versus which is x2 does not matter)

Now we just need to find our correspoding y values.  To find y1, plug x1 = 2 into our original equation:

y = x² + 2x

y = 2² + 2(2) = 4 + 4 = 8

So, y1= 8.

Similarly for y2: plug x2 = 5 into the original equation:

y = x² + 2x

y = 5² + 2(5) = 25 + 10 = 35.

So, y2 = 35

Now, plug all of our values into the rate of change equation:

(y2 – y1)/(x2 – x1) = (35 – 8 ) / (5 – 2) = 27/3 = 9.

The average rate of change of y as x changes from 2 to 5 is 9.

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