Verify Rolles theorem for the function `f(x)=x(x-3)^2,\ 0lt=xlt=3` .

Explanation

To verify Rolle's Theorem for the function \( f(x) = x(x-3)^2 \) on the interval \( [0, 3] \), we will follow these steps:

### Step 1: Check the conditions of Rolle's Theorem

Rolle's Theorem states that if a function \( f \) is continuous on the closed interval \([a, b]\) and differentiable on the open interval \((a, b)\), and \( f(a) = f(b) \), then there exists at least one \( c \) in \((a, b)\) such that \( f'(c) = 0 \).

1. **Function Definition**:
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