I have gotta some disputes regarding my problem. Can someone please help me out. I'm really strucked into it. Let a function \(f(x)\) be defined From \(\mathbb{R}\rightarrow \mathbb{R}\)

\[f(x)=x^{3}+3x^{2}+4x+b\sin(x)+c\cos(x)\]

For all \(x~\epsilon ~\mathbb{R}\), \(f(x)\) is a One-to-One function.

Find the maximum value of \[b^{2}+c^{2}\]

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TopNewestYou want \(3x^2+6x+4+b\cos x - c\sin x \ge 0\) from derivative but that's about as far as I could go. – Daniel Liu · 2 years, 3 months ago

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@Rajat Bisht see the comment I made on Calvin's dispute on the disputes page of your problem. – Daniel Liu · 2 years, 3 months ago

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The answer is, as Calvin Lin points out, 607.6. This can be worked out only by numerical means. – Michael Mendrin · 2 years, 3 months ago

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@Michael Mendrin please help me out – Rajat Bisht · 2 years, 3 months ago

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