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Unformatted text preview: , 4 , 0) . 3 Problem 3. (15 points) Let z = f ( x, y ) , where x = r cos θ and y = r sin θ, Find ∂z/∂r and ∂z/∂θ. Problem 4. (15 points) Let f ( x, y ) = x 2 y 3y 4 . Find the directional derivative of the function f at the point (2 , 1) in the direction of the vector < 3 ,2 > . 4 Problem 5. (15 points) Find the points on the surface given by x 2 + 2 y 2 + 3 z 2 = 1 where the tangent plane is parallel to the plane 3 xy + 3 z = 1 . 5 Problem 6. (20 points) Find the extreme values of the function f ( x, y, z ) = xyz where x 2 + 2 y 2 + 3 z 2 ≤ 6 . 6...
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This note was uploaded on 12/22/2008 for the course MATH 226 taught by Professor Kamienny during the Fall '07 term at USC.
 Fall '07
 KAMIENNY
 Math, Calculus

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