Calculate, estimate, and interpret average rate of change for advanced function types.
Find the average rate of change of a function on a closed interval
Problem
Find the average rate of change of \(f(x)~=~2^x\) on \([1,~4]\).
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What this problem is really about
Exponential growth is uneven, but average rate over a closed interval still depends only on its two endpoints. Evaluate each exponential output, form matching output and input differences, and keep the quotient exact. This secant slope summarizes the net rise per input unit without claiming the function changed at a constant rate between the endpoints.
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