Functions Question 345
Question: If f is a real- valued differentiable function satisfying $ |f(x)-f(y)|\le {{(x-y)}^{2}},x,y\in R $ and $ f(0)=0 $ , then $ f(1) $ equal
[AIEEE 2005]
Options:
A) 2
B) 1
C) ?1
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
$ \underset{x\to y}{\mathop{\lim }},| \frac{f(x)-f(y)}{x-y} |\le \underset{x\to y}{\mathop{\lim }},|x-y|or|f’(x)|\le 0 $
$ \Rightarrow f’(x)=0\Rightarrow f(x) $ is constant, As $ f(0)=0 $ \ $ f(1)=0 $ .
BETA
