Functie de grad 3

[maxim bogdan]

Determinati \( a\in\mathbb{N}^{*} \) si \( b,c,d\in\mathbb{R} \) astfel incat:

\( |ax^3+bx^2+cx+d|\leq 2, \ \forall\ x\in [-2,2]. \)

[Marius Mainea]

Notand \( f(x)=ax^3+bx^2+cx+d \) avem

\( 12a=|f(2)-f(-2)-2f(1)+2f(-1)|\le 12 \) de unde \( a=1 \)