Why should the gradient be 0 at a critical point?

rivasguss9
2022-08-08
Answered

Why should the gradient be 0 at a critical point?

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burgesia1w

Answered 2022-08-09
Author has **11** answers

Why should the gradient be 0 at a critical point?

asked 2022-07-20

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

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 2022-08-31

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

asked 2022-07-27

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

$\frac{dx}{dt}=x+2y+2\mathrm{sin}y$

$\frac{dy}{dt}=-3y-x{e}^{x}$

$\frac{dx}{dt}=x+2y+2\mathrm{sin}y$

$\frac{dy}{dt}=-3y-x{e}^{x}$

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 2022-07-21

In order to find the minimum/ maximum point of a function, I would take it's derivative and find critical points, points where the derivative is zero or undefined, and then put them on a number line and do strawberry field. If it's negative to the left of the point and positive to the right of the point, the point is a minimum, etc. When the denominator of your fraction is equal to zero, isn't that where you have a vertical tangent line and not a candidate for a min/max 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 $x\in \mathbb{R}$.