Folks,

If given p =3 and q=6 any numbers and the set $\displaystyle \{f \in \mathbb[C} [a,b]: p\ge f(x) \le q \forall x \in [a,b]\} $

Is my graph of f(x)=x^3 +3 shown in this wolfram link correct based on this set?

plot y(x)=x^3+3 between 3 and 6 - Wolfram|Alpha

1) What norm is this C[a,b] is representing...is it a sup norm, taxi cab norm?

2) What is the effect if the C[a,b] with sup norm is required?

Thanks