Say, If I have a function $f(x_1, x_2, x_3)$ and I know the value and derivatives of multiple combination of points. e.g. $f(0,0,0)$, $f(1,1,1)$, $f(2,3,4)$, $f(10, 20, 30)$.
What is the best way to calculate $f(5,10,15)$? We can simplify this to $2$ variables or we can ignore $2$nd order partial derivatives impact.
What would be most accurate way of getting the result? Can I do average of derivatives?