Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [stationary-point]

A stationary point is a point on a graph of a function where the derivative of the function is zero. This tag is for questions involving the existence and classification of stationary points. For questions focusing on minimizing of maximizing values under constraints, use (optimization).

A stationary point is a point on a graph of a function where the derivative of the function is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). Stationary points are used for finding minimum and maximum values of functions within a domain and for curve sketching. This tag is for questions involving the existence and classification of stationary points. For questions focusing on minimizing of maximizing values under constraints, use .

153 questions
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Saddle point integration. Null second derivative

I need to calculate an integral by the saddle point method. $I=\int_0^\infty dt\, f(t)\, e^{i S(t)}$. Notice that in my case $S(t)$ has not the typical form $S(t)=\lambda g(t)$, with a parameter $\lambda \rightarrow \infty$ . Instead, it has the…
Francisco
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Proving that a function has exactly four stationary points

I have the following function $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ defined by $$f(x,y)=xy(x+y-1).$$ Using the property that the gradient in the stationary points is zero I calculated the four stationary points: $$(0,0), (0,1), (1,0),…
Anabella Woud
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counterexample for a DC critical point that is not a limiting-stationary point?

Let $f$ be a DC function defined by $f = g - h$ where $g$ and $h$ are proper, lower semicontinuous and convex functions from $\mathbb{R}^n$ to $\mathbb{R}\cup\{+\infty\}$. A point $x^*$ is called a DC (Difference-of-convex) critical point if $0\in…
kaienfr
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Find the stationary points

Determine the stationary points of the following function and for each stationary point determine whether it is a local maximum, local minimum or a point of inflexion. $f(x)=x^3(x-1)^2$ Using product rule to find $dy/dx$ I got: $5x^4-8x^3+3x^2$…
Ahsan
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Find the stationary points of: $V=(2/r^3)-(3/r^2)$

I've applied the exponent rules and differentiated to get to the point where i have $$dr/dv=-6r^{-4}+6r^{-3}$$ I'm starting to get very confused with the math when i set the LHS = 0 in order to find the value of stationary points. Any guidance…
RocketKangaroo
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Find the stationary points of the function $f(x) = x^2 + y^2$ subjected to constraints

Find the stationary points of the function $f(x) = x^2 + y^2$ subjected to the constraint $$ x^2 + y^2 + 2x - 2y +1 =0.$$
daniel marvin
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Find the stationary point and its nature.

To find the stationary point I have to find dy/dx=0 so far I reached until this point where I'm not sure how to get the 2 X values: dy/dx= how to find the stationary points from here?
Ahsan
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derivative of matrix transpose

I am trying to calculate stationary point x* by calculating the first derivative of function $f(x) = c^T x +1/2 x^T Hx$ and find out whether it is a minimizer of f. I wrote the part with $c^T x$, also I am not sure about that, too. Could you please…
serife gizem baci
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Find and classify the stationary points of $y = x^ 2/(x-4)$

I have already obtained the answer by using the quotient rule and so there are stationary points at x = 0 and x = 8. I am fine at doing these types of questions but I don't fully understand the meaning behind the answer. This was also provided in…
Cinna
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