Calculate, estimate, and interpret average rate of change for advanced function types.
Find the average rate of change of a function on an interval by evaluating the endpoints
Problem
Find the average rate of change of \(f(x)~=~\sqrt{x}\) on \([1,~9]\).
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What this problem is really about
For a square-root function, check that both interval endpoints are in the domain before evaluating them exactly. Average rate is the difference of those two square-root outputs divided by the difference of the original inputs; subtraction does not move inside the radical. Read the reduced quotient as the slope of the secant joining the endpoint points.
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