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6 changes: 2 additions & 4 deletions meanValueTheorem/exercises/meanValueTheorem4.tex
Original file line number Diff line number Diff line change
Expand Up @@ -29,14 +29,12 @@
\]
\begin{exercise}
Compute the average rate of change of the population during the time interval $[0,4]$.
\begin{hint}
Recall, the average rate of change of the population during the time interval $[0,4]$ is given by the expression $\frac{P\left(\answer{4}\right)-P\left(\answer{0}\right)}{4-0}$.
\end{hint}

The average rate of change of the population during the time interval $[0,4]$ is $\answer{20}$ million cells per week.
\end{exercise}
\begin{exercise}
Suppose that the function $P$ is continuous on $[0,10)$ and differentiable on $(0,10)$. Then on the interval $[0,4]$ the function $P$ \wordChoice{\choice[correct]{satisfies}\choice{does not satisfy}} the conditions of the Mean Value Theorem so \wordChoice{\choice[correct]{there exists}\choice{there does not necessarily exist}} a $0<c<4$ such that $P'(c)$ equals the above calculated average rate of change of the population.

That means that at the time $t=c$ the \textbf{instantaneous rate of change} of the population is equal to the \textbf{average rate of change} of the population during the time interval $[0,4]$.
\end{exercise}
\end{document}
\end{document}