I need a little bit of help with a question.

Whats the second degree taylor polynomial (taylor vector quadratic) for the function

f(x) = x1^3 x2^2 about the point [2, 3] <------- Vector

Thanks if anyone can help

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- Nov 19th 2010, 04:46 AMnicolas123Second degree taylor polynomial help
I need a little bit of help with a question.

Whats the second degree taylor polynomial (taylor vector quadratic) for the function

f(x) = x1^3 x2^2 about the point [2, 3] <------- Vector

Thanks if anyone can help - Nov 19th 2010, 11:33 AMFernandoRevilla
It is rather difficult to understand what function you are referring to. Perhaps you mean:

At any rate:

Regards.

Fernando Revilla - Nov 19th 2010, 12:32 PMHallsofIvy
Another way to do it:

A**polynomial**already is a Taylor's polynomial. To get it around (2, 3) (which is NOT a vector), let and , so that and . Then .

To get the second degree polynomial, just drop all terms where the exponents sum to 3 or larger, then replace u and v with and again.