Compare functions represented algebraically, graphically, numerically, or verbally.
Compare average rates across representations
Problem
On \([0,~2]\), compute the endpoint values and average rates of change of \(f(x)~=~x^2\) and \(g(x)~=~2x~+~1\), then compare the rates.
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What this problem is really about
Average rates are comparable only when they use the same interval. Find each function's output change between the shared endpoints, divide by the common input change, and keep the endpoint values separate from the rates themselves. Then compare the two secant slopes, not just the final outputs.
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