A) 1
B) ?1
C) \[\infty \]
D) does not exist
Correct Answer: D
Solution :
\[f(x)=\left\{ \begin{align} & \,\,\,1\,\,\,\,\,\,\,\,\,\,\,\forall x<0 \\ & 1+\sin ,\,\,\,\forall \,0\le x<\frac{\pi }{2} \\ \end{align} \right.\] \[\therefore \,\,f'(x)=\left\{ \begin{align} & \,\,\,0,\,\,\,\,\forall \,x<0\,(\text{LHD}) \\ & \cos x,\,\,0\le x\le \pi /2,\,\,(\text{RHD}) \\ \end{align} \right.\] \\[f'(0)=\left\{ \begin{align} & \,\,0\,\,\,\,,\,\,x<0 \\ & \cos 0=1 \\ \end{align} \right.\], \\[f'(0)\] does not exist.
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