Consider the function $f(x) = x^{2/3}(6-x)^{1/3}$. Which of the following statements is false?
- A. $f$ is increasing on $(0,4)$
- B. $f$ is decreasing on $(6, \infty)$
- C. $f$ has a point of inflection at $x = 0$
- D. $f$ has a point of inflection at $x = 6$
✅ Correct Answer: $f$ has a point of inflection at $x = 6$
Explanation
$f'(x) = \frac{4-x}{x^{1/3}(6-x)^{2/3}}$ Hence $f$ increases on $(0,4)$ and decreases for $x>4$ Concavity does not change at $x = 6$
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