Mean Value Theorem

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Summary:

Program to create Mean Value Theorem

Mean Value Theorem

Prinz Azir 30 Nov 2015 23:49

Hello, I am having trouble trying to create a program for the Mean Value Theorem. My code looks like this:

Define LibPub meanval(a, b)=
Func
Return solve(d/dx(f1(x)) = (f1(b) - f1(a))/(b-a),x)|a<x<b
EndFunc
I then hit menu 2, 1 (to check syntax and store), then when I move over to the other side of the screen to test my code, I start by setting f1(x) = e^x + ln(x). Then, I try meanval(2, 4), and if my program works correctly, it will give me an answer of 3.163, but instead I get a jumbled mess:
x * (2.718282)^x - 23(lots of decimals) = 0.

Can someone help me and point out what is wrong? Thank you for your time.

Last edited on 30 Nov 2015 23:54 by Prinz Azir Show more

Re: Mean Value Theorem

jonbush 01 Dec 2015 02:26

I haven't tested this, but it may work:

Define LibPub meanval(a, b)=
Func
Return solve(d/dx(f1(x)) = avgRC(f1(x), a, b-a), x)
EndFunc

Re: Mean Value Theorem

Prinz Azir 01 Dec 2015 02:50

I tried it out with the same test if meanval(2, 4) and the returned statement from your program was
x * (2.718282)^x = -1

Interesting approach! I've never used avgRC before.

Re: Mean Value Theorem

jonbush 01 Dec 2015 03:17

Actually, I think you might need to use nSolve()

Define LibPub meanval(a, b)=
Func
Return nSolve(d/dx(f1(x)) = avgRC(f1(x), a, b-a), x)
EndFunc

Last edited on 01 Dec 2015 03:25 by jonbush Show more

Re: Mean Value Theorem

Prinz Azir 01 Dec 2015 03:23

Tried nSolve() (replacing solve) and got "No Solution found"

Re: Mean Value Theorem

jonbush 01 Dec 2015 03:27

Make sure that d/dx() is returning an expression, and avgRC() is returning a number.

Re: Mean Value Theorem

Prinz Azir 01 Dec 2015 03:30

Actually, what I did was I went back to my original code and just got rid of the |a<x<b, and got a numeric result -
x = 0.044 and x = 3.16.

Not EXACTLY what I was looking for, but I'm OK piping in my head, so to speak. Thanks for all the help!

Re: Mean Value Theorem

jonbush 01 Dec 2015 03:34

Sorry I didn't actually solve the problem. I need to get an Nspire to mess around with :)

Re: Mean Value Theorem

Prinz Azir 01 Dec 2015 03:39

No problem at all - and if you wanted to get an Nspire, I'd highly recommend Nspire CAS, pretty cheap on Amazon (cheaper than an 89!), I believe I got mine for $60 new, which was quite the bargain, and it does everything the CAS CX does, minus the color (but c'mon, who needs color anyway?).

Also, if I pipe f1(x) e.g. in the problem I'd pipe it f1(x) = e^x + lnx |2<=x<=4, it effectively pipes out the result too, even when applying the program - so I think it is quite effective!

Re: Mean Value Theorem

jonbush 01 Dec 2015 03:50

Oh, can you use solve()|a<x and x<b ?