Find the extreme values of f(x, y) = y^2-x^2

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Suresh Chand · Accepted Answer

Solution: Here f = f(x, y) = y2 - x2 Then fx = -2x,  fy = 2y And fxx = -2, fxy = 0, fyy = 2, fyx = 0 For stationary point, set fx = 0                    And                 fy = 0 or,    -2x = 0                                or,    2y = 0 or,    x = 0                                    or,    y = 0 And at (x,y) = (0, 0) (i) fxx = -2 < 0 (ii) (begin{vmatrix} f_{xx} & f_{xy} f_{yx} & f_{yy} end{vmatrix} = begin{vmatrix} -2 & 0 0 & 2 end{vmatrix}=-4 < 0) This means f ha neither extrema

Find the extremes values of f(x, y) = y² – x²

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Find the extremes values of f(x, y) = y2 – x2

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Find the extremes values of f(x, y) = y² – x²