Definition:Stationary Point/Function of Two Variables
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Definition
Let $f: \R^2 \to \R$ be a real-valued function of $2$ variables.
Let $P \in \tuple {x_0, y_0}$ be a point in $\R^2$.
$P$ is a stationary point if and only if both:
| \(\ds \valueat {\dfrac {\partial f} {\partial x} } {x \mathop = x_0}\) | \(=\) | \(\ds 0\) | ||||||||||||
| \(\ds \valueat {\dfrac {\partial f} {\partial y} } {y \mathop = y_0}\) | \(=\) | \(\ds 0\) |
Sources
- 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $4.$ Mathematics: $4.4$ Differential calculus: $\text {(vi)}$ Stationary points of $\map f {x, y}$