Find the average rate of change of f(x) = x squared + 3x on the interval from 1 to 5.

1. Work out the output at each end of the interval first. 2. At x equal to 5, the square is 25 and 3 times 5 is 15, so the output is 40. 3. At x equal to 1, the square is 1 and 3 times 1 is 3, so the output is 4. 4. The change in output is 40 minus 4, which is 36. 5. The change in input is 5 minus 1, which is 4. 6. Dividing gives 36 over 4, which is 9. 7. The answer 36 stops at the change in output and never divides. 8. The answer 4 reports the change in input instead of the ratio. 9. The answer 11 averages the two outputs rather than comparing their change. _Source: OpenStax College Algebra (CC BY 4.0), section 3.3 Rates of Change and Behavior of Graphs_