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\textbf{Math 225: Calculus III}
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\textbf{Quiz 4}\quad \textsl{Feb. 18/20, 1997}
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\item 
Imagine yourself walking on top of the graph of $f(x,y) = x^2 y + x^3 + x
y^2$. When you are over the point $(1,1)$, which direction is the steepest
climb: the positive $x$-direction or the positive $y$-direction? (Justify
your answer!).
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\item 
Let $z = y^3 \sin(x^2 + y)$. Suppose $x = g(u,v)$, $y = h(u,v)$, $g(0,0) =
\sqrt{\pi}$, $h(0,0) = \pi$, and
$$ \d{x}/du = -2, \quad \d{x}/dv = 3, \quad \d{y}/du = 5, \quad \d{y}/dv = -1$$
Compute $\d{z}/du$ at $(u,v) = (0,0)$.
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