# Limiting range

Calculus Level 4

$$f(x) = a + \sqrt{ - x^2 - 4 x }$$ , $$g(x) = 1 + \frac{4x}{3}$$.

When $$x \in [-4, 0 ]$$, it is always true that $$f(x) \leq g(x)$$.

What is the biggest value of $$a ^3$$?

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