If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)=-x^{2}-2 c x+b^{2} \), such that \( \min f(x)\max ...

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If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)=-x^{2}-2 c x+b^{2} \),
such that \( \min f(x)\max g(x) \), then the relation between \( b \) and \( c \), is
[One Correct Option, 2003]
(a) No real value of \( b \) and \( c \) (b) \( 0cb \sqrt{2} \)
(c) \( |c||b| \sqrt{2} \)
(d) \( |c||b| \sqrt{2} \)
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