\magnification = \magstep1
\nopagenumbers
\leftline{Mathematics 241 -- Multivariable Calculus}
\leftline{Quiz 7 -- November 8, 2013}
\medskip
\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
\bigskip
\noindent
A) (20) Using the method of Lagrange Multipliers, find the maximum and minimum values of $f(x,y) = 2x + 3y$ on 
the constraint curve
$$E = \{(x,y) \mid x^2 + {y^2\over 9} = 1\}.$$
(If you run into trouble with the algebra, for more partial credit, sketch what the level curves of $f$ 
should look like at the maximum and minimum together with the constraint curve.)
\bye
