# 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 \( a ^3 \)?

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

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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