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The problem asks to determine, through **Rolle's Theorem**, if the function \( f(x) = 2x^3 - 3x^2 - 2x + 2 \) satisfies the conditions of the theorem over the interval \([0, 2]\), and to analyze whether there exists at least one point \( c \in (0, 2) \) such that \( f'(c) = 0 \).

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1. **Check Continuity and Differentiability**:
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A través del Teorema de Rolle, determina si la función y = 2x^3 - 3x^2 - 2x + 2 es continua en el intervalo [0, 2], derivable en el punto (0, 2), si f(2) = f(0), y analizar si existe al menos un punto c ∈ (0, 2) tal que f'(c) = 0.

Using Rolle's Theorem, determine if the polynomial function y = 2x^3 - 3x^2 - 2x + 2 is continuous and differentiable over the interval [0, 2]. Analyze whether there exists a point c such that f'(c) = 0.

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