Using Taylor series expansions to predict $f(2)$ from a base point at $x=1$ for the following function, what is the least order $($the fewest number of terms$)$ that will provide the true value? $($Hint: at higher orders than this, the derivative of the function is $0).$

$f(x)=4x^4-2x^2+x-1$

Zero order $($one term$)$

First order $($two terms$)$

Second order $($three terms$)$

Third order $($four terms$)$

Fourth order $($five terms$)$

Fifth order $($six terms$)$

Sixth order $($seven terms$)$