Functions Question 448
Question: Let $ f(x)= \begin{cases} & 1\forall x<0 \\ & 1+\sin x,\forall 0\le x\le \pi /2 \\ \end{cases} . $ , then what is the value of $ f’(x) $ at $ x=0 $
[Orissa JEE 2005]
Options:
A) 1
B) ?1
C) $ \infty $
D) does not exist
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)= \begin{cases} & ,1,\forall x<0 \\ & 1+\sin ,,\forall ,0\le x<\frac{\pi }{2} \\ \end{cases} . $
$ \therefore f’(x)= \begin{cases} & ,0,\forall ,x<0,(LHD) \\ & \cos x,0\le x\le \pi /2,(RHD) \\ \end{cases} . $ \ $ f’(0)= \begin{cases} & 0,x<0 \\ & \cos 0=1 \\ \end{cases} . $ , \ $ f’(0) $ does not exist.
BETA
