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\leftline{Mathematics 241 -- Multivariable Calculus}
\leftline{Quiz 4 -- October 5, 2007}
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\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
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A) (5)  Let $f : {\bf R}^2 \to {\bf R}$ be the function $f(x,y) = x^3 - 2 x y^2$.
Find the equation of the tangent plane to the graph $z = f(x,y)$ at the point
$(1,1,-1)$.  
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B) (5)  Let $g : {\bf R}^2 \to {\bf R}^2$ be the function $g(s,t) = (s + t^2, st + t)$.
Find the derivative matrix $D(g)$.  
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