# Get help with critical point problems

Recent questions in Critical Point
Carsen Patel 2022-08-12

### Do have an example of a function $f:{R}^{2}\to R$ that has a critical point that is neither a saddle point nor a local (or global) extremum?

allucinemsj 2022-08-09

### Find Critical point and nature$4x\left({x}^{2}+{y}^{2}-1\right)=0$$4y\left({x}^{2}+{y}^{2}+1\right)=0$

rivasguss9 2022-08-08

### Determine the nature and stability of the critical point (0,0) for the following system:$\frac{dx}{dt}=x+2y+2\mathrm{sin}y$$\frac{dy}{dt}=-3y-x{e}^{x}$

Nathalie Fields 2022-07-24

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

Taniya Burns 2022-07-22

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

makaunawal5 2022-07-21