Tagged Questions

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How to find max and min bounds of a uncertain function

First I would like to say that I have searched the for uncertain fitting, robust fitting, linear optimization, convex optimization, etc. But I'm lacking the knowledge to solve this problem, and I need ...
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A function with positive Hessian at a critical point, without having a minimum there

I have a problem with a little instance: $f(x,y) = \begin{cases} (x^4-3x^2y^2+y^2)/(x^2+y^2) & otherwise \\ 0 & \text{(x,y)=(0,0)} \end{cases}$ This is a example of a function which ...
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find extrema of $2-\left(z-\sqrt{x^2+y^2}\right)^2+\left(z-\sqrt{x^2+y^2}\right)^3$

$$f(x,y,z)=2-\left(z-\sqrt{x^2+y^2}\right)^2+\left(z-\sqrt{x^2+y^2}\right)^3$$ Find maximum and minimum of the function.
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Method of Lagrange multipliers to find all critical points of a function

I am having difficulties in understanding the steps/method required to find the critical points of a function using the method of Lagrange multipliers. I have read through my text book and tried my ...
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Second derivative test inconclusive, all derivatives are 0, moving critical point to origin, no result?

Here is a function $f(x,y)=x^4 + 6x^2y^2 + y^4 -4x^3 - 12xy^2 + 6x^2 + 6y^2 - 4x + 1$. I've happily proved that $(1,0)$ is a critical point for that function. Now I'd like to decide whether is it a ...
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The minimum of $\int_a^b |f(t)-x|\,\mathrm{d}t$ over $x\in \mathbb {R}$

I found this statement in a book, given without proof and left as an exercise to the reader. Theorem: Suppose $f$ is a continuous and strictly increasing function on $[a,b].$ Let $m=(a+b)/2$. ...