Unformatted text preview: f at P in the direction of the vector 3 i + 4 j . (b) Find the maximal directional derivative of f at P . (Not the direction in which f increases most rapidly, but the maximal possible value of D u f (2 , 1) as u varies.) (c) Find an equation of the plane tangent to the graph z = f ( x, y ) at the point (2 , 1 , 16). [20] 4. Find all critical points of the function f ( x, y ) = x 3 + y 26 xy and determine whether each is a local maximum, local minimum, or saddlepoint. [20] 5. Use the method of Lagrange multipliers to ﬁnd the absolute maximum and minimum values of f and the points at which they occur when f ( x, y ) = x 24 y is restricted to the circle x 2 + y 2 = 25....
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This note was uploaded on 04/04/2010 for the course MATH 113 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Math, Algebra

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