Functions Question 448
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 $
[Odisha JEE 2005]
Options:
1
?1
C) $ \infty $
D) does not exist
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)= \begin{cases} & ,1,\forall x<0 \\ & 1+\sin x,,\forall ,0\le x<\frac{\pi }{2} \\ \end{cases} . $ $ \therefore f’(x)= \begin{cases} 0, & ,x<0,(LHD) \ \cos x, & 0\le x\le \pi /2,(RHD) \ \end{cases} . $ \ $ f’(0)= \begin{cases} 0, & x<0 \ 1, & x=0 \ \end{cases} . $ , \ $ f’(0) $ exists and is equal to 1.
BETA
