$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Let $A\subseteq\mathbb{R}^n$, $f:A\to\mathbb{R}^m$, and $\vec{a}\in \text{int}(A)$. Then $\vec{a}$ is a saddle point of $f$ if $\vec{a}$ is a critical point and for any $\delta>0$, there exists $\vec{x}, \vec{y}\in B_{\delta}(\vec{a})$ such that $f(\vec{x})

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So includes graph of $x^3$ at $0$ I believe?

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Let $A\subseteq\mathbb{R}^n$, $f:A\to\mathbb{R}^m$, and $\vec{a}\in \text{int}(A)$. Then $\vec{a}$ is a saddle point of $f$ if $\vec{a}$ is a critical point and for any $\delta>0$, there exists $\vec{x}, \vec{y}\in B_{\delta}(\vec{a})$ such that $f(\vec{x})

Concepts

So includes graph of $x^3$ at $0$ I believe?

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
Let $A\subseteq\mathbb{R}^n$, $f:A\to\mathbb{R}^m$, and $\vec{a}\in \text{int}(A)$. Then $\vec{a}$ is a saddle point of $f$ if $\vec{a}$ is a critical point and for any $\delta>0$, there exists $\vec{x}, \vec{y}\in B_{\delta}(\vec{a})$ such that $f(\vec{x})

Concepts

So includes graph of $x^3$ at $0$ I believe?

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
Let $A\subseteq\mathbb{R}^n$, $f:A\to\mathbb{R}^m$, and $\vec{a}\in \text{int}(A)$. Then $\vec{a}$ is a saddle point of $f$ if $\vec{a}$ is a critical point and for any $\delta>0$, there exists $\vec{x}, \vec{y}\in B_{\delta}(\vec{a})$ such that $f(\vec{x})

Concepts

So includes graph of $x^3$ at $0$ I believe?

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results