Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Compare average rates of change over the same interval
Problem
Compare the average rates of change of \(f(x)=2x+1\) and \(g(x)=x^2\) over \([1,3]\).
Big Picture
What this problem is really about
Average rates are comparable only when both functions use the same interval endpoints. We’ll evaluate each function at those endpoints, find its output change, and divide by the shared input change. This turns each function into a secant slope over the interval, so the resulting rates can be compared on equal footing.
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