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MA 227, Spring, 2010 CALCULUS III
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TEST II
10 questions, 10 points each.SHOW ALL YOUR WORK! CIRCLE YOUR ANSWER!
Question 1 Find the gradient of the function f (x, y) = xexy^ at the point (2, 0).
Question 2 Find the directional derivative of the functionvector ~v = ~i โ 2 ~j + 2~k at the point (1, 2 , 0). f (x, y, z) = xz โ xy in the direction of the
Question 3 Find local maximum, minimum and saddle points (if any) of the function f (x, y) = 2x^2 + 4xy โ y^2 + 6x โ 5.
Question 6 Let f (x, y) = xy โ x^2 y and x = s โ t, y = s^2 t. Find partial derivatives โfโs and โfโt.
Question 7 Let f (x, y) = x^2 y โ xy^2 and x = t^2 , y = 3t. Find derivative dfdt.
Question 8 Find equation of the tangent plane to the surface x^2 + 2y^2 โ 3 z^2 = 3 at the point (2, โ 1 , 1).
Question 9 Find the maximum rate of change ofdirection does it occur? f (x, y) = x^2 y + 2โy at the point (2, 1). In which
