Unformatted text preview: b) If the climber walks northeast, will she ascend or descend? At what rate? c) In what directions could she begin walking to travel a level path? 4. f ( x, y ) = ± y 3 x 2 + y 2 , if ( x, y ) 6 = (0 , 0) , if ( x, y ) = (0 , 0) . Find the directional derivative of f at (0 , 0) in the direction of (1 , 1). 5. Consider the surface x 2 + y 2z 2 = 0. Find the equation of the tangent plane to the surface at the point (3 , 4 , 5). 6. Find the equation of the tangent plane to the surface xzyz 3 + yz 2 = 2 at (2 ,1 , 1). 7. Prove that the level curves of the functions f and g deﬁned by f ( x, y ) = y x 2 , x 6 = 0 g ( x, y ) = x 2 + 2 y 2 intersect orthogonally....
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 Fall '08
 WOLCZUK
 Derivative, Rate Of Change, Vector Space, Equals sign

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