# [SOLVED] Taylor Polynomial approximation

• Jun 13th 2009, 05:33 PM
diroga
[SOLVED] Taylor Polynomial approximation
What cubic Taylor Polynomial best approximates \$\displaystyle x^4 + 2x^3 +3x - 3\$ near x = 2

take the derivative three times, plug in the value 2 for x in each derivative, divide that by i! ...

\$\displaystyle P_3(x) = 35 + 59(x - 2) + 36(x - 2)^2 + 10(x - 2)^3\$

Am I correct?
• Jun 13th 2009, 05:38 PM
apcalculus
Maple says
\$\displaystyle 10x^3-24x^2+35x-19\$
• Jun 13th 2009, 06:31 PM
diroga
Quote:

Originally Posted by apcalculus
Maple says
\$\displaystyle 10x^3-24x^2+35x-19\$

I think that maybe expanded and simplified.
• Jun 13th 2009, 06:40 PM
arbolis
Quote:

Originally Posted by diroga
I think that maybe expanded and simplified.

Yes \$\displaystyle 35 + 59(x - 2) + 36(x - 2)^2 + 10(x - 2)^3\$ and \$\displaystyle 10x^3-24x^2+35x-19\$ are equal. According to Mathematica.
• Jun 13th 2009, 07:47 PM
apcalculus
Wolfram Alpha does a pretty neat job with these kinds of tasks: Type expand 35+ 59(x-2)+ 36(x-2)^2+ 10(x-2)^3 and it spits out the expanded form.

http://www76.wolframalpha.com/input/?i=expand+35+%2B+59(x-2)+%2B+36(x-2)^2+%2B+10(x-2)^3
• Jun 13th 2009, 07:59 PM
arbolis
Quote:

Originally Posted by apcalculus
Wolfram Alpha does a pretty neat job with these kinds of tasks: Type expand 35+ 59(x-2)+ 36(x-2)^2+ 10(x-2)^3 and it spits out the expanded form.

http://www76.wolframalpha.com/input/?i=expand+35+%2B+59(x-2)+%2B+36(x-2)^2+%2B+10(x-2)^3

Thanks. I tried it but instead of typing "Expand" I typed "simplify" and I didn't get anything interesting.
• Jun 13th 2009, 08:22 PM
diroga
Thanks everybody. Is there a way I can mark this as solved?
• Jun 13th 2009, 08:23 PM
arbolis
Quote:

Originally Posted by diroga
Thanks everybody. Is there a way I can mark this as solved?

Yes. Look at the top of the thread : "Thread Tools", then "Mark this thread as solved".
• Jun 13th 2009, 08:39 PM
diroga
so thats what that tab is for :)