Today:
- Announcements
- Homework returned: p. 977, #12, 40, 54
- #12: make sure to verify your assertion with a calculation of $D$
- #40: There's an example in the text of the same problem.
- #54: Straight-forward: replace $r=1-p-q$.
- I've pushed back the due date on the Lagrange homework to Tuesday,
since we're still working on it.
- We'll start with a Lagrange multiplier example; then
we'll talk briefly about integration before beginning our quiz.
- Consider the following function:
\[
f(x,y)=4-x^2
\]
We want to maximize this function subject to
\[
g(x,y)=3x-2y=1
\]
At want point does the maximum occur?
- Draw a contour plot of $f$ (by hand). Make your plot big!
- Add a graph of the constraint equation.
- Solve using Lagrange multipliers (by hand). What is the value of
$\lambda$?
- Explain why you didn't need to do so much work....
- Now, for something different: what if I asked you to tell me the
volume of the object bounded by the graph of $f$, the $xy$-plane, and
the planes $y=0$ and $y=2$?
- How would you calculate the exact answer, and
- How might you go about approximating the answer, if
the exact answer were not apparent?
- Links:
Website maintained by Andy Long.
Comments appreciated.