Step-by-step Solution:

Given the function: \[ f(x) = x^{\frac{2}{3}} \cdot (6 - x)^{\frac{1}{3}}. \] The derivative of \( f(x) \) is computed as: \[ f'(x) = x^{\frac{2}{3}} \cdot \frac{1}{3} \cdot (6 - x)^{-\frac{2}{3}} + \frac{2}{3}(6 - x)^{\frac{1}{3}} x^{-\frac{1}{3}}. \] Simplifying further: \[ f'(x) = x^{-\frac{1}{3}} \cdot (6 - x)^{-\frac{2}{3}} \cdot \left(-\frac{x}{3} + \frac{2}{3}(6 - x)\right). \] Rearranging the terms: \[ f'(x) = \frac{1}{x^{\frac{1}{3}}(6 - x)^{\frac{2}{3}}} \cdot \left(-\frac{x}{3} + 4 - \frac{2x}{3}\right). \] Simplifying the expression inside the parentheses: \[ f'(x) = -\frac{1}{x^{\frac{1}{3}}(6 - x)^{\frac{2}{3}}} \cdot (x - 4). \] Point of Inflection The function has a point of inflection at \( x = 0 \).