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Statement 1: Let f: RvecR be a real-valu...

Statement 1: Let `f: RvecR` be a real-valued function `AAx ,y in R` such that `|f(x)-f(y)|<=|x-y|^3` . Then `f(x)` is a constant function. Statement 2: If the derivative of the function w.r.t. `x` is zero, then function is constant.

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To solve the problem step by step, we need to analyze the given statements and derive the conclusion based on the properties of differentiable functions. ### Step-by-Step Solution: 1. **Understanding the Given Condition**: We are given that for a function \( f: \mathbb{R} \to \mathbb{R} \), the condition \( |f(x) - f(y)| \leq |x - y|^3 \) holds for all \( x, y \in \mathbb{R} \). 2. **Rearranging the Inequality**: ...
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