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.