Proposition: each saddle point is a isolated critical point.

Find a counterexample to disprove it

Find a counterexample to disprove it

Carsen Patel
2022-08-12
Answered

Proposition: each saddle point is a isolated critical point.

Find a counterexample to disprove it

Find a counterexample to disprove it

You can still ask an expert for help

Trevor Copeland

Answered 2022-08-13
Author has **21** answers

Proposition: each saddle point is a isolated critical point.

Find a counterexample to disprove it

Find a counterexample to disprove it

asked 2022-08-09

Find Critical point and nature

$4x({x}^{2}+{y}^{2}-1)=0$

$4y({x}^{2}+{y}^{2}+1)=0$

$4x({x}^{2}+{y}^{2}-1)=0$

$4y({x}^{2}+{y}^{2}+1)=0$

asked 2022-07-23

Determine the total number of critical points of the function $f(x)=(x+{e}^{x}{)}^{k}$, where $k>0$ is an integer

asked 2022-07-14

What is the basic idea for finding critical point via Morse theory and critical groups?

asked 2022-07-24

Determine the nature and stability of thecritical point (0,0) for the following system:

$\frac{dx}{dt}=-\mathrm{sin}(x-y)$

$\frac{dy}{dt}=1-5y-{e}^{x}$

$\frac{dx}{dt}=-\mathrm{sin}(x-y)$

$\frac{dy}{dt}=1-5y-{e}^{x}$

asked 2022-08-31

Find all the critical points of f when $f(x)={x}^{4/5}(x-{5}^{2})$

asked 2022-08-14

I am given a $3$ variable function:

$f(x,y,z)=\mathrm{cos}(xy)+\mathrm{cos}(yz)+\mathrm{cos}(zx)$

How to do the Hessian matrix for a $3$ variable function.

$f(x,y,z)=\mathrm{cos}(xy)+\mathrm{cos}(yz)+\mathrm{cos}(zx)$

How to do the Hessian matrix for a $3$ variable function.

asked 2022-07-22

Suppose $f:\mathbb{R}\to \mathbb{R}$ has two continuous derivatives, has only one critical point ${x}_{0}$, and that ${f}^{\u2033}({x}_{0})<0$. Then $f$ achieves its global maximum at ${x}_{0}$, that is $f(x)\le f({x}_{0})$ for all $x\in \mathbb{R}$.