APPM 2350 Midterm: appm2350spring2015exam2_sol
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Appm 2350 - spring 2015 - exam 2 solutions: the following questions are unrelated. For parts (a)-(d), answer either always true or not always true. No justi cation necessary. (a) if fx and fy do not exist at a point p , then f (x, y) is discontinuous at p . False: consider the function f (x, y) = |x| + |y|. True: a saddle point exhibits this phenomenon exactly. (c) if f (x, y) is a continuous function, then there exists some direction u such that the directional derivative of f in the direction u is zero. False: there may be extrema in the interior of the constrained domain which will not be captured through. Lagrange multipliers: consider the function f (x, y) = 6x2 2x3 + 3y2 + 6xy (a) find, and if possible, classify all critical points of the function f (x, y). If you can"t classify a critical point, write.