Let `f: RvecR` be a function satisfying condition `f(x+y^3)=f(x)+[f(y)]^3fora l lx ,y in Rdot` If `f^(prime)(0)geq0,` find `f(10)dot`

Explanation

To solve the problem step by step, we will analyze the given functional equation and derive the required result.

### Step 1: Analyze the functional equation
We are given the functional equation:
\[ f(x + y^3) = f(x) + [f(y)]^3 \]
for all \( x, y \in \mathbb{R} \).

### Step 2: Substitute \( x = 0 \) and \( y = 0 \)
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