# Thread: [SOLVED] Taylor Polynomial approximation

1. ## [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?

2. Maple says
$\displaystyle 10x^3-24x^2+35x-19$

3. Originally Posted by apcalculus
Maple says
$\displaystyle 10x^3-24x^2+35x-19$
I think that maybe expanded and simplified.

4. 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.

5. 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

6. 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.
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