Active Prelude to Calculus

Compute \(f(1+h)\) and expand and simplify the result as much as possible by combining like terms.

Determine the most simplified expression you can for the average rate of change of \(f\) on the interval \([1,1+h]\text{.}\) That is, determine \(AV_{[1,1+h]}\) for \(f\) and simplify the result as much as possible.

Compute \(g(1+h)\text{.}\) Is there any valid algebra you can do to write \(g(1+h)\) more simply?

Determine the most simplified expression you can for the average rate of change of \(g\) on the interval \([1,1+h]\text{.}\) That is, determine \(AV_{[1,1+h]}\) for \(g\) and simplify the result.