calcolo della derivata errato - perchè?

lemma_farkas shared this question 3 years ago

Answered

In questo file ho voluto "simulare" la corsa tra 2 runner che hanno equazioni orarie differenti. Voelvo mostrare il concetto di derivata come coeff angolare della tangente. Ho riscontrato però questo problema :

il runner rosso ha eq g(x)=4*cubicroot(x^2) e funziona tutto

il runner verde ha eq f(x)= -1+ e^(alfa x) dove alfa è un parametro settato a 0.03. Il problema è che ho chimato la costante m=f'(t) dove t è lo slider del tempo che scorre. Qui è il problema la derivata non torna . Se t=100 allroa dovremmo avere f'(100)=0.03*exp(0.03*100)= (da calcolatrice) 0,6 mentre ggb mi dà il valore di 0,74 come mai ?

Grazie mille in anticipo

Files: runner.ggb

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Comments (14)

mathmagic ● 3 years ago

select view rounding to 10 decimals

you'll see why

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lemma_farkas ● 3 years ago

It doesn't change that much... For example if t=100, f'(100) still remains near that value, which is 0.7419170905

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jumera ● 3 years ago

rounding 10 decimals

you don't look what you have to look...

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jumera ● 3 years ago

Scrivi nell'inserimento

Derivata(f)

è esatto f'(10) = 0.7419170905

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rami ● 3 years ago

Consider the definition of f(x).

The factor is not 0.03. The factor is 0.031570229324762.

(when check on the pocket-calculator)

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jumera ● 3 years ago

On a eu une belle journée ici en France...

Toi aussi rami..?

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rami ● 3 years ago

I'm not sure. In quarantine, you can't see the perfidies so well.

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jumera ● 3 years ago

perfidies???

just waiting for our poster's answer...

0c0c18c0e88215447e317f250a2e292a

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rami ● 3 years ago

What is the Problem?

Maybe the language: "tückisch" in German was (automatically) translated to "perfides", which can be misleading.

But what was intended: I gave you three answers to choose from.

For me the quarantine/lockdown is "tückisch" (because, I think, it seems to give supposed security).
Even the unnoticed rounding is "tückisch" for me (because he is not easily recognized)
And also your question could (conditional !!) be "tückisch" (because for me, completely out of context, And if knowingly out of context: then my anwer is comparable with your question)

You don't have to answer, but I would be interested to know why you ask me (late at night !) about the weather.

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jumera ● 3 years ago

"I would be interested to know why you ask me (late at night !) about the weather."

I give you three answers to choose from.

I didn't watch TV to see wheather in your country
I am a bad boy very perfide, always posting out of context
We (mathmagic, me and you) gave enough clues to lemma_farkas, and wait for answer (and hope he find the solution : very much better he find solution than other give full solution)

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lemma_farkas ● 3 years ago

I really thank you for your suggestion

The problem involves what I called alfa, which is not exactly 0.03 as I supposed. So the exp function gets bigger and bigger with this value.

Am I right ? Or am I still wandering in the dark?

:-) thank you in advance

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jumera ● 3 years ago

Good... You understood

Now everything correct or it doesn't do what you want..?

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lemma_farkas ● 3 years ago

yes it does. My problem has been with my students when I illustrate the geometrica meaning. Our calculation didm't match geogerba's one. But now, thanks to all of you, I can clarify the mistery

Bye bye all of you, I really appreciate your effort

See you sono :D

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jumera ● 3 years ago

Happy for you...

Have a nice day (here today, some clouds...)

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