[tex]y=3x^4+1\\
y'=12x^3\\\\
12x^3=0\\
x=0\leftarrow \text{stationary point}\\\\
\forall x\in(-\infty,0)\ y'<0\Rightarrow y\searrow\\
\forall x\in(0,\infty)\ y'>0\Rightarrow y\nearrow\\
\Downarrow\\
y(0)=y_{min}[/tex]
[tex]y_{min}=3\cdot0^4+1=1[/tex]
