Assignment 9 – Midterm 2 Review Lab
Due Date: November 1, 2011
1. Consider the equation for population of beavers in Tailslap pond given in #2 of the old midterm.
Write a script in R to plot the function, exact first derivative, and exact second derivative side by
side in the same figure. Label your figures B(t), B’(t), and B’’(t). (You can use the approximate
derivatives to check your calculations but you do not need to include them in your plots for this
assignment.) Save your figure as a jpeg and include it in your report. Include your script in
your report as well.
What does the plot of the first derivative tell you about the shape of B(t)?
What does the plot of the second derivative tell you about the shape of B(t)?
According to this equation, will the population of beavers ever go extinct?
2. Write a new equation for the population of beavers that has a critical point at t = 3 with your
second derivative given by
. (Hint: Think about how first and second derivatives
relate to each other and try to work backwards from the graph of B’’(t). There is more than one
right answer for what B(t) could be.) Include your new equation for B(t) in your assignment.
Change your script in R to plot this new function and it’s exact first and second derivatives side
by side. Save your figure as a jpeg and include it in your report. You do not need to include
your script again for this problem!
What does the plot of the first derivative tell you about the shape of B(t)?
What does the plot of the second derivative tell you about the shape of B(t)?
According to this equation, will the population of beavers ever go extinct?