MHB Taylor Series: Find 2nd Degree Series for x^2+y^2=4 at [1, -\sqrt[]{3}]

[Anewk]

How would I find the second-degree Taylor series for $$x^2+y^2=4$$ at $$[1, -\sqrt[]{3}]$$?

 

[MarkFL]

Hello and welcome to MHB! :D

Can you tell us what you've tried so we know where you are stuck or what you may be doing wrong? We can offer better help that way.

 

[Prove It]

How would I find the second-degree Taylor series for $$x^2+y^2=4$$ at $$[1, -\sqrt[]{3}]$$?

The second degree Taylor polynomial for a function $\displaystyle \begin{align*} f(x) \end{align*}$ centred at the point is $\displaystyle \begin{align*} (h, k) \end{align*}$ is $\displaystyle \begin{align*} f(x) = f(h) + f'(h) \, \left( x - h \right) + \frac{f''(h)}{2} \, \left( x - h \right) ^2 \end{align*}$.

Can you evaluate $\displaystyle \begin{align*} f(1), f'(1), f''(1) \end{align*}$?