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Q1 - Find the critical points of the function f(x,y) = x^2 + 2y^2 - x^2y and then classify them into relative maxima, relative minima and saddle points.
Q2 - Let f(x,y) = xy - x - y + 3 and R is the triangular region with vertices (0, 0), (2, 0) and (0, 4). Find the interior and boundary points only at which the absolute extrema of f(x,y) can occur.
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Let f(x,y)=x^2+2y^2-x^2y and then classify them into relative maxima, relative minima and saddle points
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Q1 - Find the critical points of the function f(x,y) = x^2 + 2y^2 - x^2y and then classify them into relative maxima, relative minima and saddle points.
Q2 - Let f(x,y) = xy - x - y + 3 and R is the triangular region with vertices (0, 0), (2, 0) and (0, 4). Find the interior and boundary points only at which the absolute extrema of f(x,y) can occur.
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which gives stationary points of (0,0) (2,1) (-2,1)
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forming the hessian matrix:
---- first stationary points (0,0)
both eigenvalues are positive, so (0,0) is a local minimum
---- second stationary point (2,1)
one eigenvalue is negative, one is positive, so (2,1) is a saddle point
---- third stationary points (-2,1)
same eigenvalues as previous stationary point, so (-2,1) is also a saddle point:
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(0,0) is a local minimum
(2,1), (-2,1) are saddle points
The Beginning Of All Things To End.
The End Of All Things To Come.
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