Simplifying equations

BUMPRW shared this problem 9 years ago

Please excuse my computer/excel lingo, but I don't think this editor supports an equation editor.

When solving for the second derivative of x*sqrt(x+1) geogebra's result was (3x+4)/(sqrt(x+1))*(4x+4).

When simplified the result should read (3x+4)/(4*(power(x+1,1.5))

Not sure this is fixable, but thought I should mention it

1

Currently, the CAS, which is good, is basically a work in progress.

The TI-Nspire does the following

So GG"s simplification in this case seems very good to me.

Thanks

Tony

1

Since Geogebra is suppose to be an education program and the goal is to teach students proper practices, in my world good engineering practices, then why would you want a "seems good to me" answer. I certainly wouldn't compare my company's standards of performance to that of another company. Additionally, and you should realize this, if you are programming you want equations in their simplest form; otherwise, often you find, but not always, that you are wasting CPU time and adding the chance of potential error. . . .off the soapbox, I guess so much for preaching . . . still a timesaver

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Both GeoGebra and the TI-Nspire are educational/professional tools and my comparison was to illustrate the point CAS programs do not all process solutions the same way.

why would you want a "seems good to me" answer.
This seemingly good solution allows teachers a teachable moment to illustrate technology is just a tool to assist the user over some of the difficult situations in computation, but as a user we need to be aware of the need to be able to consider and an answer viable in different formats. {my soapbox}

Technology is a time-saver and I would not like to go back to my youth without it.

Tony

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(3x+4)/(sqrt(x+1))*(4x+4).

(3x+4)/(4*(power(x+1,1.5))

In fact you can argue that either one is the "simplest form". The concept of "simplest form" is not well-defined.

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Hi

I agree with Murkle.

By the way, for a student who does not know anything about non integer exponents, (3x+4)/(sqrt(x+1))*(4x+4) is the simpliest form ;=)

Laurent

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Just FYI, not sure what you entered into your NSPIRE CAS, but I don't think it was f(x)=x*(sqrt(x+1)). Your answer made me do a double take. I checked the simplification on an HP 50G and it appears to be off, and didn't match Geogebra or any of my calculators. I did check the double derivative on a TI-89 Titanium and TI NSPIRE CX CAS and they matched after they were simplified . . .again I verified the simplification on the HP 50G . . . which also doesn't simplify the answer completely, but close enough. Also checked the answer on the HP 50G and it matched after it was simplified, although it was slightly different.

Really apologize for bringing this up and my aversion to "close enough". Your program is a great timesaver and is in fact close enough. I was just wondering if you could get it that itty bit closer. My wife is the math teacher, I just double/triple check the lesson plans and examples. So, I agree that simplification, to some degree, is in the eyes of the beholder. Geogebra is an excellent aide.

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:flushed: I re-entered it into the Nspire, I probably did make a typo originally. :flushed: It gave your result, but GG did give the correct result just not as simplified. However, as was mentioned, how do you define "simplified."

Tony