Calculate, estimate, and interpret average rate of change over an interval.
Use average rate of change to find a missing endpoint value
Problem
Use the average rate of change information to find the missing endpoint value: average rate from \(x=2\) to \(x=6\) is \(3\) and \(f(2)=5\).
Big Picture
What this problem is really about
A known average rate converts the interval’s input change into an output change. We’ll write the endpoint change quotient with the missing output, substitute the known endpoint value, and solve the resulting equation. A final substitution check should reproduce the given rate, catching the common mistake of multiplying by the ending input instead of by the interval length.
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