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I want to confirm this:

a=8 , b=5 , c=7

Decide the Taylor polynomial of degree 2 in the point (0, a) to the function f (x, y)=sqrt(1+bx+cy). Decide with the aid of Taylor polynomial if the function has a local minimum in (0, a).

I used the partial derivates:

df/dx = 5/(2*sqrt(1+5x+7y)) = 5/sqrt(57)

df/dy = 7/(2*sqrt(1+5x+7y)) = 7/sqrt(57)

and so on with the rest of the derivates

And with the all derivates in the taylor polynomial i will get a value different then 0 and that mean that it havent got a minimum.

Is this the correct way to slove this?