If x+|y|=2y, then y as a function of x, at x=0 is

Question

If $x+|y|=2y$, then $y$ as a function of $x$, at $x=0$ is

Accepted Answer

For $y\ge0$: $x+y=2y\Rightarrow y=x$ (need $x\ge0$ for $y\ge0$... actually $y=x/1$ giving $y=x$); for $y<0$: $x-y=2y\Rightarrow y=x/3$.

So $f(x)=\begin{cases}x, & x\ge0\x/3, & x<0\end{cases}$, continuous at $0$ (both give $0$), but LHD $=\dfrac13
e$ RHD $=1$ --- not differentiable at $0$.

Solutions · 1