Question

Find the stationary point on the curve y=3x^4 +1 and determine its nature

Answer 1

`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\\earrow\\ \Downarrow\\ y(0)=y_(min)`


`y_(min)=3\cdot0^4+1=1`