Calculate, estimate, and interpret average rate of change for advanced function types.
Find the average rate of change of a function on an interval
Problem
Find the average rate of change of \(f(x)~=~1/x\) on \([1,~4]\).
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What this problem is really about
Before forming a reciprocal secant slope, verify that the entire interval avoids the input where the function is undefined. Then evaluate both endpoints and keep the nested fraction organized as one output difference divided by one input difference. The sign should agree with whether the reciprocal graph rises or falls across that valid interval.
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