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Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z, y) subject to the constraint g(z,y) = 0 which is a closed curve with g € C'. Suppose as well that Vg(a, b) +0 at all points along the curve g(z, y) =0. If the global minimum value occurs at (a, b), then which of the following statements are true? Select all true statements. At (a, b), the level curve of f passing through O (a, 6) is tangent to the constraint curve g(z, y) 0. O Vf(a, b) = Vg(a, b) for some Ae R At (a, b), Vg(a, b) and Vf(a, b) are pointing at O either in the same direction or in opposite directions. None of the above

Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z, y) subject to the constraint g(z,y) = 0 which is a closed curve with g € C'. Suppose as well that Vg(a, b) +0 at all points along the curve g(z, y) =0. If the global minimum value occurs at (a, b), then which of the following statements are true? Select all true statements. At (a, b), the level curve of f passing through O (a, 6) is tangent to the constraint curve g(z, y) 0. O Vf(a, b) = Vg(a, b) for some Ae R At (a, b), Vg(a, b) and Vf(a, b) are pointing at O either in the same direction or in opposite directions. None of the above

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z,y) subject to the constraint g(z,y) = 0 which is a closed curve with g € C'. Suppose as well that Vg(a, b) +0 at all points along the curve g(z, y) =0. If the global minimum value occurs at (a, b), then which of the following statements are true? Select all true statements. At (a, b), the level curve of f passing through O (a, b) is tangent to the constraint curve g(z, y) = 0. O V/(a, b) = AVg(a, b) for some A E R. At (a, b), Vg(a, b) and Vf(a, b) are pointing at O either in the same direction or in opposite directions. O None of the above
Transcribed Image Text:Suppose we wish to use the Method of Lagrange Multipliers to minimize a differentiable function f(z,y) subject to the constraint g(z,y) = 0 which is a closed curve with g € C'. Suppose as well that Vg(a, b) +0 at all points along the curve g(z, y) =0. If the global minimum value occurs at (a, b), then which of the following statements are true? Select all true statements. At (a, b), the level curve of f passing through O (a, b) is tangent to the constraint curve g(z, y) = 0. O V/(a, b) = AVg(a, b) for some A E R. At (a, b), Vg(a, b) and Vf(a, b) are pointing at O either in the same direction or in opposite directions. O None of the above
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