Calculate, estimate, and interpret average rate of change for quadratic functions.
Find a missing endpoint value from an average rate of change
Problem
The average rate of change of \(f\) from \(x~=~2\) to \(x~=~6\) is \(5\), and \(f(2)~=~3\). Find \(f(6)\).
Big Picture
What this problem is really about
A known average rate can be used backward to recover a missing endpoint output. We’ll place the unknown in the difference quotient, turn rate times input change into the total output change, add that change to the starting output, and verify the result in the original rate equation.
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