# Global maxima of \(f(x)\)

**Calculus**Level 5

A function \(f(x)\) is defined for non negative real numbers.It has its range as the set of real numbers.Given that \(f(x) \) is twice differentiable in its domain.Also, \(f(0)=-3 \) and the value of first derivative at \(x=0\) is 4. It is given that the sum of \(f(x)\) and second derivative of \(f(x) = -x|\sin x|\) times the first derivative of \(f(x)\),

What is the maximum value of \( f(x) \)?