Math Problem Statement
find the critical points in f(x,y) = xsiny and their type
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Critical Points
Partial Derivatives
Hessian Matrix
Second Derivative Test
Formulas
Partial derivative: f_x(x, y) = sin y, f_y(x, y) = x cos y
Second partial derivatives: f_{xx} = 0, f_{yy} = -x sin y, f_{xy} = cos y
Hessian determinant: det(H) = -cos^2 y
Theorems
Second Derivative Test
Hessian Matrix Classification of Critical Points
Suitable Grade Level
Undergraduate Calculus
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