[tex]\it f'(x) =4x\\ \\ g'(x)=-2x+1\\ \\ f'(x)\geq g'(x) \Rightarrow 4x\geq-2x+1 \Rightarrow 4x+2x\geq1 \Rightarrow 6x\geq1 \Rightarrow \\ \\ \Rightarrow x\geq\dfrac{1}{6} \Rightarrow x\in\Big[\dfrac{1}{6},\ \infty\Big)[/tex]
[tex]\it b)\ f'(x)+f(x) =g'(x) \Rightarrow 4x+2x^2+1=-2x+1 \Rightarrow 2x^2+6x=0 \Rightarrow \\ \\ \Rightarrow 2x(x+3)=0 \Rightarrow \begin{cases}\it x+3 =0 \Rightarrow x_1=-3\\ \\ \it2x=0 \Rightarrow x_2=0\end{cases}[/tex]
