Mathematics 241 – Multivariable Calculus Quiz 4 – October 5, 2007

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A) (5) Let f : R^{2} → R be the function f(x, y) = x^{3} − 2xy^{2}. Find the equation of the tangent plane to the graph z = f(x, y) at the point (1, 1, −1).

B) (5) Let g : R^{2} → R^{2} be the function g(s, t) = (s+t^{2}, st+t). Find the derivative matrix D(g).