**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 (y_{2} – y_{1})/(x_{2} – x_{1})

So far, we have x_{1} = 2 and x_{2} = 5

(the order of which is x_{1} versus which is x_{2} does not matter)

Now we just need to find our correspoding y values. To find y_{1}, plug x_{1} = 2 into our original equation:

y = x² + 2x

y = 2² + 2(2) = 4 + 4 = 8

So, y_{1}= 8.

Similarly for y_{2}: plug x_{2} = 5 into the original equation:

y = x² + 2x

y = 5² + 2(5) = 25 + 10 = 35.

So, y_{2} = 35

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

(y_{2} – y_{1})/(x_{2} – x_{1}) = (35 – 8 ) / (5 – 2) = 27/3 = 9.

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