How Do You Obtain the Fixed Points and Stability of a Piecewise Function?

How do you obtain the fixed points and stability of a piecewise function?

I think you are confusing fixed points and critical points. Fixed points have nothing to do with the derivative being $0$, and there is typically no way to find a fixed point other than just solving the equation $f(x)=x$. The second fixed point $x=frac12-beta$ comes from solving $f_beta(x)=x$ in the second case of the definition of $f_beta$. Similarly, stability of fixed points has nothing to do with the second derivative. You can instead test for stability using the first derivative. The idea is that if $|f'(x)|>1$ then $f$ is changing faster than $x$ is so if you perturb $x$ a little away from the fixed point then $f$ will move farther away. On the other hand, if $|f'(x)|1$ at a fixed point then the fixed point is unstable and if $|f'(x)|

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Should a woman over 50 still wait to marry for love if the opportunity for financial stability comes first?

Yes. Financial stability that's completely dependent on someone else, let alone someone you are not sure you like enough to spend the rest of your life with if Mr. Right does come along, is not stability at all

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how does "MARRIAGE" bring stability to a child?

i agree with 'queen of beer' lol. shes right. i think loving caring parents bring stability, not necessarily being married.

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Stability and reactivity of carbocations?

You are right. Perhaps counter-intuitively, you will see more reactions with participation of ternary carbocations because they are less reactive. Unlike the more reactive ones, ternary carbocations can actually exist long enough to enter various reactions (E1/Sn1/rearrangements) instead of being a short-lived intermediate

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Financial Stability Oversight Council (FSOC)

In addition to chairing the NCUA board, Matz was one of ten voting members on FSOC. Created by the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010, FSOC identifies risks between 2010 and 2016 to the financial stability of the United States, promotes market discipline, and responds to emerging risks between 2010 and 2016 to the stability of the United States' financial system.

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How to fix puncture in stability ball?

Their are patches for inflatable products. Look for a repair kit in the swimming pool section of your local department store. You could also use a bicycle tire repair kit or a water bed repair kit.

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Stability of superoxides of alkali metals

Well according to my book 'General and inorganic chemistry volume 2, by Dr. Ivan Filipovic & Dr. Stjepan Lipanovic ', the oxidation state of superoxides is -1/2. $ceK$, $ceRb$ and $ceCs$ react with oxygen and form type $ceMO2$ compounds called superoxides. They are ionic crystalised compounds containing cation $ceM$ and anion $ceO^2-$, and since the oxygen anion has 13 valent electrons, superoxides are colorful, paramagnetic, and unstable compounds, and they also exist only in solid state

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What laptop do you enjoy most?

Macbook. Because of its sleek design, reliability and stability

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no image stabilization in my camera?

I've got one lens with image stabilization. As much as I love it, I usually leave it at home or in the camera bag, because other lenses serve my needs better. Image Stabilization can help steady a photographer, but it is also used to make up for bad habits. What did we all do before this technology came along? We learned how to hold our cameras, select the proper shutterspeed and ISO, and freeze the moment. You can learn to do the same, if you have the mind to.

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System Stability: Can we derive stability of a discrete system (Frequency domain, Z-transform) by applying analogous methods?

If you use the bilinear transform to map from s-plane poles and zeros to z-plane poles and zeros, the left-hand half-plane of the s-plane will be mapped to the inside of the unit circle on the z-plane. This preserves stability because on s-plane the requirement for stability is that poles are on the left-hand half-plane and on the z-plane it is that they are inside the unit circle. I did not examine too carefully your s and z-domain formulas, but indefinite integration is marginally stable with a pole at the origin of the s-plane, or on the unit circle of the z-plane. Implemented as a nonrecursive filter:$$textout[i] = textin[i-N textin[i-N dots textin[i- textin[i],$$integration over $N$ samples is stable. Implemented as a recursive filter: $$textout[i] = textout[i- textin[i] - textin[i-N],$$it is stable in fixed-point arithmetic, but can drift if implemented in floating point arithmetic due to accumulation of numerical error. Even then it can be stabilized by moving the pole slightly inside the unit circle, or by periodically resetting the filter state by calculating it using the nonrecursive filter. But sample and hold is about taking an input sample and keeping the output at that value for some time. That can be programmed directly and gives no stability problems

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