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Differentiabilty

The continuou...

Question

The continuous function $f (x, y)$ is said to have saddle point at $(a, b)$ if

Where the subscripts $x, y$ etc. denote partial derivatives.

f_{x} (a, b) = f_{y} (a, b) = 0;

f_{x y}^{2} - f_{x x} f_{y y} < 0

(a, b)

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f_{x} (a, b) = 0; f_{y} (a, b) = 0;

f_{x y}^{2} - f_{x x} f_{y y} > 0

(a, b)

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f_{x} (a, b) = 0; f_{y} (a, b) = 0;

f_{x x}

and

f_{y y} < 0

(a, b)

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f_{x} (a, b) = f_{y} (a, b) = 0;

f_{x y}^{2} - f_{x x} f_{y y} < 0

(a, b)

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Solution

The correct option is B $f_{x} (a, b) = 0; f_{y} (a, b) = 0;$
$f_{x y}^{2} - f_{x x} f_{y y} > 0$ at $(a, b)$
$∵$ at saddle point $r t - s^{2} < 0$

Suggest Corrections

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⌊ a / b ⌋

⌊ ⌋

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