Question

If for a function f, |f(x) – f(y)| £ (x – y)² ∀ x, y Î R, then f is –

• A. Strictly increasing
• B. Strictly decreasing
• C. Constant
• D. Strictly increasing when x > 0

Answer 1

Answer: (C)

Constant

Answer 2

**Sol. |**f(x) – f(y)| £ (x – y)²

$\lim _ { y \rightarrow x }$ $\frac{|f(x)–f(y)|}{|x–y|}$ £ $\lim_{y \rightarrow x}$ |x – y|

̃ |f ¢(x)| £ 0 ̃ f¢(x) = 0

̃ f(x) is a constant function