Math 155-004, Quiz 9
March 31, 2009
NAME:
Instructions: This quiz is closed books and closed notes. You may use calculators. Work that is erased or
crossed out will not be graded. Show your work for full credit.
1. (3 pts) x∗ =
3
5
is an equilibrium for the discrete-time dynamical system
xt+1 =
5
xt (1 − xt ).
2
Using the Stability Theorem, is this equilibrium stable, unstable, or neither?
2. (3 pts) Consider the Logistic Growth Model xt+1 = rxt (1 − xt ). What condition on r guarantees that
the equilibrium r∗ = 0 is stable?
3. (4 pts) Identify all the local and global maxima and minima of the function f (x) = x3 − 3x + 1 on the
interval 0 ≤ x ≤ 3. Give your answers as coordinates (as in “There is a global max at (2,5).”).
Extra Credit: In recent years, researchers studying the physics of the human circulatory system have
moved toward computer models that use software tools handed down form the
industry to solve fluid mechanics equations.