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Topic review (newest first)

SteveB
2013-06-11 06:21:27

The cubic equation for dy/dx=0 was:

0 = 12x^3 + 3(k-18)x^2 + (64-12kx) + 8k-48

The DELTA discriminant for whether this cubic equation has:
3 distinct real roots when DELTA > 0
multiple root with all roots real when DELTA = 0
or one real root and two complex conjugate roots when DELTA < 0
(Source: Wikipedia entry for cubic polynomial equations)

Using an algebraic package you can solve this for k where DELTA = 0

So DELTA = 432k^4 + 12096k^3 + 83520k^2 - 345600k - 3998208

I then used a grapical calculator with a polynomial of order 4 solver to get numerical solutions:
Two of them were complex conjugates of (-12.1161977552, +/- 3.62069124665) these are irrelevant for this analysis.
The real solutions are relevant, one of them was Bob's k = 5.9536152399
The other was also mentioned by Bob earlier to less accuracy and I am getting: k = -9.72121972948
These solutions for k indicate that there is a multiple root with all roots real and a graph shows that they have two stationary points
in terms of the original quartic expression involving x and k. One is an inflection and the other a minimum.
You could work out whether there are 3 turning points or 1 turning point for the ranges either side and in between these
if you wanted to give a full analysis of how many turning points you get for all values of real k.
(Perhaps draw a graph on a graphics calulator for the function of DELTA in terms of k and see where it is above zero
and where it is below zero. Then use the wiki quote that I gave above.)
If I am understanding this correctly there is one stationary point inbetween the two (k>-9.7212197... and k<5.9536152...)
and there are three stationary points for k < -9.721297... and for k > 5.9536152...
The exact formula for calculating the roots of k is extremely complicated and I would not like to attempt that one
without a something like Wolfram or another computer algebra package.
smile

anonimnystefy
2013-06-11 04:28:04

Discrete and discreet are not the same.

I was referring to the topic where we were having the antonym discussion.

bob bundy
2013-06-11 03:32:24

The same one as what?

You want me to respond to a topic called 'Discrete Calculus'.  This didn't ring any bells in my brain so I did a search.  No topic found.

So I looked through the recent topics list.  Still nothing.

So I asked for the url and you have said it is the same one.  Same as what.  Is this some sort of test?  Can I see the invisible words?  Am I expected to read your mind?  Is there a secret code? 

dictionary.com wrote:

dis·creet
  [dih-skreet]  adjective 
1.
judicious in one's conduct or speech, especially with regard to respecting privacy or maintaining silence about something of a delicate nature; prudent; circumspect.

...........................

ibid wrote:

cal·cu·lus
  [kal-kyuh-luhs] noun, plural cal·cu·li  [kal-kyuh-lahy] 
1.
.....................

2.
Pathology . a stone, or concretion, formed in the gallbladder, kidneys, or other parts of the body.

I get it.  smile  You are worried about my kidney stone but are trying to be discreet about it.  Too late!  I've told everyone now.  eek

Bob

anonimnystefy
2013-06-10 23:09:46

That is the same one.

bob bundy
2013-06-10 22:02:47

you haven't yet replied to the Discrete Calculus topic

What is this topic?

url?

Bob

anonimnystefy
2013-06-10 21:37:52

The other what?

bob bundy
2013-06-10 17:33:03

Stefy wrote:

By the way, you haven't yet replied to the Discrete Calculus topic and our "interesting" antonym discussion.

Antonym reply done.

Cannot find the other ???  It is being very discreet.

Bob

anonimnystefy
2013-06-10 06:48:52

What's even more interesting is that it seems there are more than one values of k which do that. If I remember correctly, something similar should happen at +/- 2sqrt(33).

By the way, you haven't yet replied to the Discrete Calculus topic and our "interesting" antonym discussion.

bob bundy
2013-06-10 04:50:28

hi Stefy

roflol   roflol   roflol

You did that on paper of course.  smile

But it's nice to know there's an exact solution.

Thanks.

Bob

anonimnystefy
2013-06-10 03:53:40

Hi Bob

I don't think you'll like seeing this one:

bob bundy
2013-06-09 04:33:51

Thank you.  smile

Bob

anonimnystefy
2013-06-09 04:32:23

Oh, you are right. I will try getting the exact answer if possible.

bob bundy
2013-06-09 04:14:43

But k is any real number so you must have checked an infinite number of cases.  I'm impressed.  smile

Did you try k= 5.95361523.....  ?

Bob

anonimnystefy
2013-06-09 03:56:54

Well, I have checked all k between -10 000 and 10 000 and in no case was there 2 stationary points.

bob bundy
2013-06-09 03:39:09

hi Stefy,

Well I thought I had.  See post 4

By all means tell me where I'm going wrong. 

Bob

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