# 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".

×