MATH 200 Midterm: MATH 200 2009 Winter Test 2
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MATH 200 Full Course Notes
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Use backs of sheets if extra space needed. Rules governing examinations (cid:149) each candidate must be prepared to produce, upon request, a. [12] 1. (a) a surface z(x, y) is de ned by zy y + x = ln(xyz). (i) compute z. Y at (x, y, z) = ( 1, 2, 1/2). 1. (b) a surface z = f(x, y) has derivatives f. Y = 2 at (x, y, z) = (1, 3, 1). (i) if x increases from 1 to 1. 2, and y decreases from 3 to 2. 6, Nd the change in z using a linear approximation. (ii) find the equation of the tangent plane to the surface at the point (1, 3, 1). [14] 2. (i) for the function z = f(x, y) = x3 + 3xy + 3y2 6x 3y 6. Find and classify [as local maxima, local minima, or saddle points] all critical points of f(x, y)
