A) \[f(x)=\left\{ \begin{align} & \frac{1}{2}-x,\,\,\,\,\,\,\,x<\frac{1}{2} \\ & {{\left( \frac{1}{2}-x \right)}^{2}},\,\,\,x\ge \frac{1}{2} \\ \end{align} \right.\]
B) \[f(x)=\left\{ \begin{align} & \frac{\sin x}{x},\,\,\,x\ne 0 \\ & \,\,\,\,\,1\,\,\,,\,\,\,x=0 \\ \end{align} \right.\]
C) \[f(x)=x|x|\]
D) \[f(x)=|x|\]
Correct Answer: A
Solution :
The function defined in option is not differentiable at \[x=\frac{1}{2}\].
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