Whats the difference between the critical point of a function and the turning point?Aren't they both just max/min points?

Marisol Rivers
2022-07-20
Answered

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tykoyz

Answered 2022-07-21
Author has **17** answers

asked 2022-11-14

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$\begin{array}{}\left({\displaystyle \frac{{\mathrm{\partial}}^{2}f(p)}{\mathrm{\partial}{x}_{i}\mathrm{\partial}{x}_{j}}}\right)\end{array}$$1\le i,j\le n$

How can we deduce that f only has finitely many non-degenerate critical points by this function only has non-degenerate critical point? And how can we use the compact manifold’s properties to solve the question?

How can we deduce that f only has finitely many non-degenerate critical points by this function only has non-degenerate critical point? And how can we use the compact manifold’s properties to solve the question?

asked 2022-07-14

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

asked 2022-10-23

Let $f:{\mathbb{R}}^{2}\to \mathbb{R}$ be a function such that

$$f(x,y)=5{x}^{2}+x{y}^{3}-3{x}^{2}y.$$

Is $(0,0)$ a local maximum, local minimum or a saddle point?

$$f(x,y)=5{x}^{2}+x{y}^{3}-3{x}^{2}y.$$

Is $(0,0)$ a local maximum, local minimum or a saddle point?

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 $x\in \mathbb{R}$.

asked 2022-10-28

Why does a nontrivial $V\to V$ have a critical point?

asked 2022-08-16

If the hessian evaluated at a critical point is positive (negative) definite, then we can conclude that it's a local minimum (maximum) there. If the hessian is indefinite (both negative and positive eigenvalues), then it's a saddle point.

What happens if the Hessian is positive SEMI-definite?

What happens if the Hessian is positive SEMI-definite?

asked 2022-11-13

If the first derivative is $0$ at a certain point, is that necessarily a critical point?