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.