Find the extreme values of f(x,y) = y2 - x2. | Mathematics I 2074

Mathematics I20745 marksNumerical: extreme values, multivariableMaximum and minimum values

Find the extreme values of $f(x,y) = y^2 - x^2$ . [5]

Find the extreme values of $f(x,y) = y^2 - x^2$. [5]

Function: $f(x,y) = y^2 - x^2$ No other numeric data required; this is a standard extremum problem. $fx = -2x, \qquad fy = 2y$ Set to zero: $-2x = 0 \Rightarrow x = 0, \qquad 2y = 0 \Rightarrow y = 0$ Critical point: $(0, 0)$ . $f{xx} = -2, \qquad f{yy} = 2, \qquad f{xy} = 0$ $$D = f{xx},f{...

Function: $f(x,y) = y^2 - x^2$ No other numeric data required; this is a standard extremum problem. $$fx = -2x, \qquad fy = 2y$$ Set to zero: $$-2x = 0 \Rightarrow x = 0, \qquad 2y = 0 \Rightarrow y = 0$$ Critical point: $(0, 0)$. $$f{xx} = -2, \qquad f{yy} = 2, \qquad f{xy} = 0$$ $$D = f{xx},f{...

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