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For a function of two variables, describe critical point.

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asked 2021-02-19
For a function of two variables, describe critical point.

Answers (1)

2021-02-21

The point (a, b) is a critical point (or a stationary point) of f(x, y) provided one of the following is true,
1.\(\displaystyle\triangledown f{{\left({a},{b}\right)}}={0}\) (this is equivalent to saying that \(\displaystyle{{f}_{{{x}}}{\left({a},{b}\right)}}={0}\ {\quad\text{and}\quad}\ {{f}_{{{y}}}{\left({a},{b}\right)}}={0}{)}\),
2.\(\displaystyle{{f}_{{{x}}}{\left({a},{b}\right)}}\ {\quad\text{or}\quad}\ {{f}_{{{y}}}{\left({a},{b}\right)}}\) doesn’t exist

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