JEE PYQ: Differentiation Question 3
Question 3 - 2021 (26 Feb Shift 1)
Let $f$ be any function defined on $\mathbb{R}$ and let it satisfy the condition: $|f(x) - f(y)| \leq |(x-y)^2|$, $\forall (x, y) \in R$. If $f(0) = 1$, then:
(1) $f(x) < 0, \forall x \in R$ (2) $f(x)$ can take any value in $R$ (3) $f(x) = 0, \forall x \in R$ (4) $f(x) > 0, \forall x \in R$
Show Answer
Answer: (4) $f(x) > 0, \forall x \in R$
Solution
$|f’(y)| \leq 0 \Rightarrow f’(y) = 0$. So $f$ is constant = $f(0) = 1 > 0$.
BETA
