# 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 $$f(x)$$?

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