Limits Continuity And Differentiability Question 116
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
Options:
A) 3
B) 4
C) 5
D) 6
Show Answer
Answer:
Correct Answer: C
Solution:
$ f’(1)=\underset{h\to 0}{\mathop{\lim }}\frac{f(1+h)-f(1)}{h}; $
As function is differentiable so it is continuous 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
