Answer the Question $f ( x , y )$ (Thin Curves) as Well as the Constraint

question 227

Multiple Choice

Answer the question.
-The graph below shows the level curves of a differentiable function $f ( x , y )$ (thin curves) as well as the constraint $g ( x , y ) = \sqrt { x ^ { 2 } + y ^ { 2 } } - \frac { 3 } { 2 } = 0$ (thick circle) . Using the concepts of the orthogonal gradient theorem and the method of Lagrange multipliers, estimate the coordinates corresponding to the constrained extrema of $f ( x , y )$ .

• A) (1.3, 0.7), (-1.3, 0.7), (-1.3,-0.7), (1.3,-0.7)
• B) (1.5, 0), (0, 1.5), (-1.5, 0), (0, -1.5)
• C) (1.1, 1.1), (-1.1, 1.1), (-1.1,-1.1), (1.1,-1.1)
• D) (1.5, 0.2), (0.7, 1.3), (-1.5, 0.2), (-0.7, 1.3), (-1.5, -0.2), (-0.7, -1.3), (1.5, -0.2), (0.7, -1.3)

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