Phrases Previous Year Questions (PYQs) – Increasing Decreasing Function

Given Function: $$f(x)=x^{2/3}(6-x{)}^{1/3}$$

• f is increasing in (0, 4): ✅ True
• f has a point of inflection at x = 0: ✅ True
• f has a point of inflection at x = 6: ✅ True
• f is decreasing in (6, ∞): ❌ False (function not defined there)

Correct Answer (False Statement): $$\boxed{{\displaystyle \text{f is decreasing in }(6,\mathrm{\infty })}}$$