a quadratic function has the following characteristics: g''(1)=6,g'(1)=3, and g(1)=1. determine a possible equation for this function.

i got g(x)=3x^2-3x+1 and was wondering if anyone can verify.

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- Sep 4th 2010, 05:48 AMeuclid2determine equation of a quadratic function
a quadratic function has the following characteristics: g''(1)=6,g'(1)=3, and g(1)=1. determine a possible equation for this function.

i got g(x)=3x^2-3x+1 and was wondering if anyone can verify. - Sep 4th 2010, 06:03 AMPlato
- Sep 4th 2010, 06:07 AMchisigma
The 'simplest' function that 'meets' the requirements is the 'Taylor polynomial'...

$\displaystyle \displaystyle g(x)= g(1) + g^{'} (1)\ (x-1) + g^{''} (1)\ \frac{(x-1)^{2}}{2}= 1- 3\ x + 3\ x^{2}$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$