MATH 226 Study Guide - Midterm Guide: Unit Disk, Bounded Function
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Be sure that this examination has 2 pages. Special instructions: no notes or calculators are allowed. Brie y justify your examples. (a) a continuous function f : d r which has no absolute maximum. Find the equation of the plane which contains (1, 2, 3) and (4, 6, 7) and is perpendicular to the plane 3x + 2y + z = 1. Find and classify all critical points of f (x, y) = x4 + y4 4xy2. [15] 6. (a) brie y explain why the function f (x, y, z) = x+y2z on its domain d = {(x, y, z) : 2x2 + y2 + z2 1} has an absolute maximum and minimum. (b) find all absolute minima and maxima of the function in (a). Evaluate: (a) the mass of a triangular plate with vertices at (0, 0), (1, 1) and (1, 3), and density f (x, y) = xy. (b) r 1.
