If \( f(x)=x^{3}+3 x^{2}+4 x+b \sin x+c \cos x \forall x \in R \) i...

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If \( f(x)=x^{3}+3 x^{2}+4 x+b \sin x+c \cos x \forall x \in R \) is a one-one function, then find the maximum value of \( \left(b^{2}+c^{2}\right) \).
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