[tex]f(x) = x^3+ax+b \\ f'(x)=3x^2+a \\ \\ $Functia are un minim egal cu 1 in punctul x = 1: \\ \rightarrow f'(1) = 0 $ (x=1, punct de extrem$) \quad $si$ \quad f_{min} = 1 \\ \\ \Rightarrow \Big\{f'(1) = 0 \quad $si$ \quad f(1) = 1\Big\} \\ \Rightarrow \Big\{3\cdot 1^2+a = 0 \quad $si $\quad 1+a+b =1 \Big\}\Rightarrow \\ \Rightarrow \Big\{a = -3 \quad $si$ \quad 1-3+b = 1\Big\} \Rightarrow \\ \Rightarrow \Big\{\boxed{a = -3} \quad $si$ \quad \boxed{b = 3}\Big\}[/tex]
