Functions Question 341
Question: Suppose $ f(x) $ is differentiable at $ x=1 $ and $ \underset{h\to 0}{\mathop{\lim }},\frac{1}{h}f(1+h)=5 $ , then $ f’(1) $ equals
[AIEEE 2005]
Options:
A) 5
B) 6
C) 3
D) 4
Show Answer
Answer:
Correct Answer: A
Solution:
$ f’(1)=\underset{h\to 0}{\mathop{\lim }},\frac{f(1+h)-f(1)}{h}; $ As function is differentiable so it is continous as it is given that $ \underset{h\to 0}{\mathop{\lim }},\frac{f(1+h)}{h}=5 $ and hence $ f(1)=0 $ . Hence $ f’(1)=\underset{h\to 0}{\mathop{\lim }},\frac{f(1+h)}{h}=5 $ .
BETA
