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Let f(x)=2x^(3)+ax^(2)+bx-3cos^(2)x is ...

Let ` f(x)=2x^(3)+ax^(2)+bx-3cos^(2)x` is an increasing function for all ` x in R ` such that ` ma^(2)+nb+18 lt 0` then the value of m+n+7 is

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To solve the problem, we start with the given function: \[ f(x) = 2x^3 + ax^2 + bx - 3\cos^2 x \] Since \( f(x) \) is an increasing function for all \( x \in \mathbb{R} \), we need to ensure that its derivative \( f'(x) \) is greater than zero for all \( x \). ### Step 1: Find the derivative of \( f(x) \) ...
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