Is this always minimum?

Calculus Level 5

Consider a function \(f\colon\Bbb R\to\Bbb R\) defined by \(f(x)=x^{3}+3x^{2}+4x+b\sin(x)+c\cos(x)\)

Given that \(f\) is one-to-one, find the maximum value of \(b^{2}+c^{2}\).

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