Question:medium
Let \( R \) be the set of all real numbers. Let \( f: R \to R \) be a function such that \( |f(x) - f(y)|^2 \le |x - y|^3, \forall x, y \in R \). Then \( f'(x) = \)
Let \( R \) be the set of all real numbers. Let \( f: R \to R \) be a function such that \( |f(x) - f(y)|^2 \le |x - y|^3, \forall x, y \in R \). Then \( f'(x) = \)
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Whenever you see $|f(x) - f(y)| \le |x - y|^k$ with $k > 1$, the function is always a constant. Its "slope" is so restricted that it cannot change at all.
Updated On: May 6, 2026
- \( f(x) \)
- \( 1 \)
- \( 0 \)
- \( x^2 \)
- \( x \)
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The Correct Option is C
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