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Re: Walking through a problem that uses a derivative

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On Sat, 16 Apr 2016 07:38:38 +0200, Friendly Neighborhood Vote Wrangler
Emeritus wrote:

> Time to spin the kooks up again. Melt, kooks, melt. <snicker>
> 
> vallor, in <news:dncv8iF8ojjU1@mid.individual.net> did thusly jump head
> first into the wood chipper again:
> 
>> On Fri, 15 Apr 2016 18:09:51 +0800, Bite My Shiny Metal Ass (aka Shiny
>> Tinfoil Spankard) wrote:
> 
>>> FNVWe stomped a retard's brain flat. Again:
> 
>>>> Bwahahahaaa! Shiny Tinfoil Spankard is now claiming that x^2 is a
>>>> trigonometric function whose value for the complement of an angle is
>>>> equal to the value of 2x of the angle itself.
> 
>> I ALREADY TOLD YOU that that isn't what a derivative is.
> 
> I know that, and you know that... perhaps you should teach Shiny Tinfoil
> Spankard what a derivative is. LOL
> 
>> The derivative gives the slope of the line tangent to the curve for
>> varying values of x.
> 
> The first derivative, yes. But then I've known that for years... stock
> trading kind of requires knowing that when you're programming your own
> indicators.
> 
>> This is useful for finding a curve's minimum or maximum (where the
>> slope will be 0).
> 
> It's useful for a lot more than that. One must find the first derivative
> before one can find the second or third, after all.
> 
>> (Hopefully this is still taught with a unit on graphing curves by hand.
>> I really don't know, maybe someone else can chime in.)
> 
>>>> What's the angle of x^2 and 2x, Shiny Tinfoil Spankard? Are you
>>>> confused, Mathematical Moron? Yeah you are. LOL
> 
>>> Rolf & Lol! with a bwahaha too.
> 
>> I'm glad you caught that, I totally missed it.  (Got just a couple of
>> paragraphs into his post, then ennui set in.)
> 
> You caught Shiny Tinfoil Spankard wondering why x^2 and 2x aren't
> co-functions?

He never did that.

> That's because he's a confused little kooktard.

Looks more like you are _very_ confused.

> Remember,
> he's the moron who confused the mathematical derivatives using stock
> trading indicators with stock options. LOL

He uses them to compute the price of tea in China.

> 
>> Let's see if we can generate a koan-like moment for the budding
>> mathematician:
>> 
>>    d/dx( 2x^3 + 69 ) = 6x^2
> 
> d/dx(2x^3 + 69) = (3*(2x)^2 + 0) = 6x^2 = 2*6x = 12x
> 
> Did you forget to simplify? LOL

That isn't "simplifying" you did, you took the second derivative.

No where in my post did I try to muddy the waters with second 
derivatives, I was talking about the basics.  Obviously.

So you get an "A" for effort, but I'm going to have to mark you down for 
being over-enthusiastic with the process.

> 
>>    d/dx( 4x^2 )      = 8x
> 
> d/dx(4x^2) = 2*(4x) = 8x
> 
>>    d/dx( 4x^2 + 7x + 3 ) = 8x + 7
> 
> d/dx(4x^2 + 7x +3) = (2*(4x) + 7 + 0) = 8x + 7
> 
>> DO YOU GET IT YET?
> 
> I always have gotten it.

Sure, sure.

> You should try teaching Shiny Tinfoil Spankard.
> LOL

I'll let you in on an open secret:

He knows more about this than you do.

> 
>> You can't fake knowing math.
> 
> Says the guy who fucked up above. LOL

Actually, no, it was you who over-enthusiastically took the second 
derivative when all we were dealing with were first derivatives.

> 
>> Prediction:  the response to this will be "jess trollin'".
> 
> Wrong. Again. LOL

Except, see below...


> 
>> Finally, the eager student asked:
> 
>>>> What's the angle of x^2 and 2x, Shiny Tinfoil Spankard?
> 
>> Since 2x is the slope of the curve tangent to f(x) = x^2 for varying
>> values of x, your question doesn't even half make sense.
> 
> That was the point, Idjit. Shiny Tinfoil Spankard asking if x^2 and 2x
> were co-functions didn't even half make sense, so I highlighted that by
> asking him a question he couldn't possibly answer because it has no
> answer.
> 
>> And I hesitate to give a sensible answer regarding 2x for a specific
>> point x, because _that_ does use trigonometry, but not for the reasons
>> you think.
>> for r = sin(theta), r is the ratio, and theta is the angle.  But let's
>> take that example of x^2 for x = 5 (picked out of thin air)
>> and see what we get:
>> 
>> x = 5 f(x) = (5)^2 = 25 d/dx( f(x) ) = 2x; for x = 5, this is 10
>> 
>> So we know a few things about that point on the curve:
>> 
>> It is at (x,y) = (5,25).
>> The slope of the point tangent to the curve at (5,25) is 10.
>> 
>> What is the slope?  It is the ratio of y/x.
>> So the "angle of 2x" for x=5 would be solved by using the trigonometric
>> function that solves for y/x ratios -- arctan.  (Remember tangents? 
>> This is a song about tangents.)
> 
> But we're not talking about the slope of x^2,

Actually, we are.  In purely mathematical terms, that's what a derivative 
is _for_.

Let's take the case of when you were dropped on your head as a child.

The formula for the distance covered is d = (1/2)At^2.

In english units, acceleration of Earth's gravity is approximately 32 ft/
sec/sec.  I'll leave off the units, and you can see how this works.

d = -16t^2

This is a parabola.  First derivative (as you point out elsewhere) give 
velocity:

s = -32t

This is a straight line, but its units are in a different frame of 
reference.  You don't plot this line with the parabola and hope to see 
something meaningful -- you use this resulting formula (the first 
derivative) to develop the formula that gives you a line tangent to the 
curve for any given x.

> we're talking about the
> slope of its derivative, for which the only two true conditions are
> [0,0] and [2,4].

I'm afraid you're still confused.

>> arctan(10)
>> 1.47112767430373459185287557176173085185530637718323
>> 
>> So there's your answer in radians, Cadet Fakey.
>> 
>> Oh, you want that in degrees?
>> 84.28940686250035748730411865176563988852083893309440
>> 
>> So the curve x^2 at that point (5,25) is about 6 degrees from vertical,
>> leaning to the right...political pun not intended.
> 
> It's just as easy to graph it.
> 
> <http://i.imgur.com/x2Z9U7s.png>
> <http://i.imgur.com/emGGhNA.png>
> 
> Gee... I got the same answers you did.

No you didn't, you graphed formulas that are only orthogonally related to 
each other.

Let me show you what it looks like closer to the origin:

x = 3
f(x) = x^2
so for the point in question, you have (3,9)
d/dx(f(x)) = 2x
so the slope of the line tangent to the curve at (3,9) is 6.

But that is the slope of the line _that passes through 3,9_.  So the 
formula for _that_ line -- the line that would make sense to graph with 
it -- is

[ insert here:  you know the formula for the line of a given slope
is y=mx+c, I hope, where "m" is the slope.  If not, then welcome to first 
semester algebra.]

y = 6x + c, where "c" is some constant to make the line pass through 
(3,9).  (That is to say, the value of y when x=0).

So solve for c:

9 = 6(3) +c
c = -9

So the line that makes sense to plot with the parabola is:

y = 6x-9

*NOW* you can start plotting:

   http://imgur.com/PMbfGPj

The _line_ I plotted is tangent to the curve at (3,9).  It passes through 
(3,9), and it's "parallel" (instantaneously) at that point.

All the derivative gives you is the _slope_ of the line I plotted -- but 
you still need to figure out the formula for the line, and that changes 
from point to point.

_That_ is how you use a derivative.  Look at the graph.  Do you see now?


> Seems I have an intuitive grasp
> on the mechanics and the mathematics of it,

I'm afraid not, you just plotted a bunch of functions that were 
orthogonally related, but not the line that would have been obvious to 
plot, given what a derivative is _for_.

Unless you can come up with some kind of utility to plotting the line 
indicated by the formula that gives you the slope of a line tangent to 
the curve at a given point, I'd have to say you're utterly at sea.

(Say...are you on a bote?)

> whereas Shiny Tinfoil
> Spankard has yet to produce even a single graph *or* correct equation.
> LOL

But he knows how to take a derivative, and doesn't call them "co-
functions" (or claim that other people are using the term when they 
clearly haven't).

> 
> Now... what's all that got to do with the fact that Shiny Tinfoil
> Spankard is a backpedaling bleatfarting blither-blathering liar
> desperately raping Google

You know, you'd get a lot farther in this process if you'd learn a little 
charity.

I'm x-posting this to afn so that interested parties that can't 
participate in this group can comment.

-- 
Won a Checky(tm) on 2016-04-15
 ...for schooling a kook about derivatives.
(Including working through a sample problem.)

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  Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop  Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-13 01:20 -0400
  Re: Our very own "chinese room" Skeet <invalid@invalid.invalid> - 2016-04-13 13:23 -0600
  Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-16 07:38 +0200
    Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-16 14:48 +0000
      Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-17 07:35 +0200
        Re: Walking through a problem that uses a derivative "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop  Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-17 01:50 -0400
          Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-17 18:08 +0000
            Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-18 07:29 +0200
              Re: Walking through a problem that uses a derivative vallor <vallor@cultnix.org> - 2016-04-18 06:24 +0000
                Re: Walking through a problem that uses a derivative Rick Sabian's Allstar Canadian Assworm Zydeco Band <Lunatic.Fringe@The.Edge> - 2016-04-17 23:28 -0700
                Re: Walking through a problem that uses a derivative Friendly Neighborhood Vote Wrangler Emeritus <FNVWe@altusenetkooks.xxx> - 2016-04-19 08:28 +0200
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    Re: fakeys meltdown Skeet <invalid@invalid.invalid> - 2016-04-16 02:27 -0600
    Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop  Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-16 11:22 -0400
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      Re: Our very own "chinese room" "\"Fakey's\" dogwhistle holder living at 5907 Stanton Ave., Pittsburgh, PA (aka Teh Mop  Jockey), socked up as 5907 Stanton Avenue, Pittsburgh, PA 15206-2117" <root@127.0.0.1> - 2016-04-17 01:53 -0400
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