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AgentJags -
post Oct 18 2007, 09:28 PM
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How do I find local max/min, concavity, and points of inflection for quartic, and cubic functions, using a table of values?


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foxshox -
post Oct 18 2007, 10:09 PM
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QUOTE(AgentJags @ Oct 18 2007, 10:28 PM) *
How do I find local max/min, concavity, and points of inflection for quartic, and cubic functions, using a table of values?

Well I am assuming you got a table with numbers plugged into an original equation, derivative and second derivative.

Your asking for a lot explained, so you might have to post of exactly what you need done(maybe scan it in). You have to plot the critical points(of the first derivative) on a number line and select points in between the points. Then if its positive put a plus above that part of the line, and same with a negative. Then to find the relative(local) max find where it changes from + slope to - slope, and for relative min find where it changes from negative slope to positive slope. Concavity is found through the second derivative. Do the exact same thing as before, and instead of the + and - representing slopes, it represents concavity. If there is a + it is concave up, and - it is concave down. And then you can find the points of inflection finding where it changes from concave up to concave done( or vice versa). The degree of the function really doesn't matter at all. You have to just have to find critical values, and plug in points between the critical values.

This is an EXTREMELY brief explanation, and since, by the sound of it, you have never done this before, I will have a really hard time believing this will help all that much.
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AgentJags -
post Oct 19 2007, 03:21 PM
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Ok. Let's say, I'm given the following:

f(x)=x^4-6x^3-12x^2+88x-96

And I am asked to:

Find the local maximum/minimum
Find the point(s) of inflection
State the intervals of increase/decrease
State the intervals of concavity (this doesn't apply for ^4's)

So I begin by making my table of values:



How would I determine the above questions?



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foxshox -
post Oct 19 2007, 05:19 PM
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Yeah uhh sorry, I have done this method, I just forgot it completely. There is another(easier) way of doing it, but I am not willing to bother trying to convey that shit over the internet unless Im getting paid or some shit, since that shit WILL take forever to explain. Hopefully somebody else will be able to help you, but this would take me a while to explain even if I was right next to you trying to explain it.
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lotd -
post Oct 19 2007, 11:50 PM
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Meh thats something new.

I'm assuming they give you a domain and are the problems given guaranteed integer critical numbers?

Increasing/decreasing should be easy to spot because basically the Y values will either be increasing/decreasing respectively. (Basically your differences will be positive for increasing and negative for decreasing)

That's all I can tell for sure by from the tables. I'm pretty sure that equation has non integer critical numbers.

Also could you just look for it using the first and second derivative test and pretend you used a table?
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deathcube -
post Dec 28 2007, 08:23 PM
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There's a very well explained method I could give to you, but as above, it would take effort and time to explain it, so, just offer me some paypal for the lesson and I'mm all yours clapping.gif
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foxshox -
post Dec 30 2007, 12:42 AM
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QUOTE(deathcube @ Dec 28 2007, 08:23 PM) *
There's a very well explained method I could give to you, but as above, it would take effort and time to explain it, so, just offer me some paypal for the lesson and I'mm all yours clapping.gif

Because of course, if you want to learn math, pay somebody on a diablo 2 website. Probably a person not even very far above this in math, no less.

This post has been edited by foxshox: Dec 30 2007, 12:43 AM
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deathcube -
post Jan 1 2008, 08:33 PM
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QUOTE(foxshox @ Dec 30 2007, 01:42 AM) *
QUOTE(deathcube @ Dec 28 2007, 08:23 PM) *
There's a very well explained method I could give to you, but as above, it would take effort and time to explain it, so, just offer me some paypal for the lesson and I'mm all yours clapping.gif

Because of course, if you want to learn math, pay somebody on a diablo 2 website. Probably a person not even very far above this in math, no less.



But not me, I'm a graduate Electronic Engineer and well although I'm not working right now as an engineer since Im taking air traffic control course, I'm still very capable in math and shit smile.gif, with the years you'll find out this was all a piece of cake and your teachers taught you the hard method instead of the easy one first smile.gif
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