# Minimum of maximum

**Algebra**Level 5

Consider all monic polynomials of the form \(f_a(x) = x + a \). As \(a\) ranges over all real numbers, what is the minimum value of \(N_a\), where

\[ N_a = \max_{x \in [-16, 10] } \lvert f_a(x) \rvert ? \]

**Details and assumptions**

The last equation states: "The maximum value of the absolute value of \(f_a(x)\), as \(x\) ranges from \(-16\) to \(10\) inclusive".