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MATH GEEKS CHALLENGE!

PenPoint
By PenPoint
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3 minutes ago, kingkickolas said:

Thanks! But is it the domain or range of h'' (or both)?

Basically domain only, but there is no specific limitation of the range.

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Posted

(Opens calculator)

wait...

i'm s**t at Maths, even though i'm asian.....

is it 21?

or am i stupid? (too late to make the joke, already made it)

****SORRY FOR MY ENGLISH IT'S REALLY TERRIBLE*****

Been married to my wife for 3 years now! Yay!

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14 minutes ago, samiscool51 said:

-snip-

If you're talking about the question I posted about an hour ago, sorry, isn't 21 :(

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So I already got an answer graphically, but I feel like that method is cheating :P so I'm gonna go for an analytical solution too

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2 hours ago, PenPoint said:

If you're talking about the question I posted about an hour ago, sorry, isn't 21 :(

i was joking, my maths skills are utter s**t, it's a miracle that i can do 1+1!

****SORRY FOR MY ENGLISH IT'S REALLY TERRIBLE*****

Been married to my wife for 3 years now! Yay!

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1 minute ago, samiscool51 said:

i was joking, my maths skills are utter s**t, it's a miracle that i can do 1+1!

So am I :'D

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@PenPoint I'm having trouble determining the coefficients of f'. If f' is written f'(x) = 4x3 + 3ax2 + 2bx + c, I conclude that c = 0, and 3a + b = -6. But I can't reduce the solution any further. I also checked graphically, and it seems that any combination of a and b that satisfies the relation 3a + b = -6 will produce an h that has a continuous h''(x). Is there a condition missing to further specify a and b (like that f has only even powers, for example)?

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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18 hours ago, PenPoint said:

@kingkickolas @Kumaresh I can confirm that there is no condition that I've missed. And according to someone's explanation, we don't even have to get the value of b. :o

By the way what is your graphical answer @kingkickolas?

Okay yeah I forgot to do one thing, so with some more work I get f'(3) = 48. Which is also what I got graphically.

It was a pretty involved calculation though! Are these problems timed?

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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Just now, Kumaresh said:

It is an extremely lengthy calculation. I gave up part way through. Based on the steps which I mentioned, what did you do additionally to get f'(3) ?

It was just a lot of shit to try before I found the thing that worked. I assume the solution could be written pretty succinctly if you know the method.

 

But what I did was find h'' just like you did: h''(x) = f''(g(x)) g'(x)2 + f'(g(x)) g''(x). Then we can see that discontinuities in h'' come from discontinuities in g' and g'' since g is not differentiable. So discontinuities in g' and g'' occur where g is not differentianble, which is at 0 (due to the |x| in g) and at the zeros of g (due to the |...| around everything). So first find the zeros of g, which occur at 7pi/18, 11pi/18, -7pi/6, and -11pi/6. (The positive zeros recur every +(2/3)pi*n and the negative zeros recur every -2pi*n, for non-negative integer n.) This breaks g into 4 regions: (1) x > 0 and x between the 2 positive zeros, (2) x > 0 and x not between the zeros, (3) x < 0 and x between the 2 negative zeros, and (4) x < 0 and x not between those zeros. In each of these regions, g is straightforward and doesn't have ugly absolute value signs. So we can differentiate g easily in these regions. Now we're finally almost done. The last thing to do is match h'' at the boundaries of each region so that it's continuous. It turns out that matching at the boundaries of regions (1) and (2) gives the same condition as matching between (3) and (4), which is that c = 0. Then when you match at the boundary of (2) and (3) (where x = 0), you get 3a + b = -6. To get the final condition, you need to show that h''(0) exists. So you do the limit definition of the derivative from the left and from the right and for the limit to exist, 4 + 3a + 2b + c = 0, which combined with the previous conditions, defines f'(x), and it's trivial to then find f'(3).

 

There must be an easier and more clever way to do this, because this took way too long haha. Much respect for the people who have to do these, damn.

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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4 hours ago, PenPoint said:

@Kumaresh @kingkickolas

Busy lately, one more day and I'll post it. Sorry for keep you all waiting :(

Hey man no prob! :)

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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8 hours ago, PenPoint said:

@Kumaresh @kingkickolas

Yay!

 

I can say that this is easier than the first one, but still both are literally puke problems :S

cal.pdf

 

As you all may expect, I still have tons of extreme questions like this. Tell me if you want more B|

Damn I was hoping there would be a really clever short solution, but you really have to go through all that ugly algebra!

 

Yeah post more if you've got em!

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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8 hours ago, PenPoint said:

@Kumaresh @kingkickolas Lost interest? :'(

 

I've actually been super busy in the last week or so, so I haven't been able to work on it that much! :( But it's an interesting problem, maybe over the weekend I'll look at it again!

My (first) build: i7 4790k | Noctua NH-U14S + NF-A15 | Gigabyte Z97X-SLI | G.Skill Ripjaws X 2x4GB 2133MHz CL9 | Samsung 840 EVO 120GB | Seagate 2TB SSHD | 2x MSI R9 270X TwinFrozr crossfire | Seasonic G Series 750W 80+ Gold | Asus VX238H 23" | GAMDIAS HERMES | Logitech G602 | Steelseries QcK | Windows 8.1

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12 hours ago, Kumaresh said:

-snip-

 

4 hours ago, kingkickolas said:

-snip-

Sorry for the rash judgement. :'(  Answer is quite far from 8 or 9, and then I think this weekend is a good time to post the answer.

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