4. Let $f(x)=x^{2}+p x+q$ where $p, q$ are some coefficients. By how much can the maximum value of the function $g(x)=|f(x)|$ differ from the minimum value of this function on the interval $[2 ; 6]$?

ANSWER: by 2.
Solution: For $f(x)=x^{2}+p x+q$ the difference between the maximum and the minimum value is at least 4 (this can be shown graphically). By choosing $q$,
we find that the maximum value of the modulus of the minimum differs by no more than 2. Example: $f(x)=(x-4)^{2}-2$.