100hw4 - (a Show that the second derivative test provides...

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Math 100 Homework 4 fall 2010 due 29/10 1. (13.6, 74) On a certain mountain, the elevation z above a point ( x, y ) in an xy-plane at sea level is z = 2000 - 0 . 02 x 2 - 0 . 04 y 2 , where x , y and z are in meters. The positive x-axis points east, and the positive y-axis north. A climber is at the point ( - 20 , 5 , 1991). (a) If the climber uses a compass reading to walk due east, will she begin to ascend or descend? (b) If the climber uses a compass reading to walk due northwest, will she begin to ascend or descend? (c) In what compass direction should the climber begin walking to travel a level path (two answers)? 2. (13.7, 16) Show that if f is diFerentiable and z = xf ( x/y ), then all tangent planes to the graph of this equation pass through the origin. 3. (13.8, 28)
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Unformatted text preview: (a) Show that the second derivative test provides no information about the critical points of the function f ( x, y ) = x 4-y 4 . (b) Classify all critical points of f as relative maxima, relative minima, or saddle points. 4. (13.8, 40) ±ind the points on the surface x 2-yz = 9 that are cloest to the origin. 5. (13.8, 42) ±ind the maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the ²rst octant on the plane x + y + z = 1. 6. (13.9, 34) ±ind the highest (one with the biggest z-coordinate) and the lowest points on the intersetion of the elliptic paraboloid z = x 2 +4 y 2 and the cylinder x 2 + y 2 = 1. 1...
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