Let $f(x)=x^2+2 b x+2 c^2$ and $g(x)=-x^2-2 c x+b^2, x \in R$. If $b$ and $c$ are nonzero real numbers such that $\min f(x)>\max g(x)$, then $\left|\frac{c}{b}\right|$ lies in the interval

• A

  $\left(\frac{1}{2}, \frac{1}{\sqrt{2}}\right)$
• B

  $\left(\frac{1}{\sqrt{2}}, \sqrt{2}\right)$
• Correct answer
  C

  $(\sqrt{2}, \infty)$
• D

  $(0,1)$

Hence, the correct answer is option: 'C'.