Show that the function `f(x)=2x-|x|` is continuous but not differentiable at `x=0`

Explanation

`f(x)=2x-x,x>=0`

`f(x)=2x-(-x),x<0`

f(x) is continuous when lim f(x)=limf(x)=f(0)

`LHL=lim_(x->0^-)(3x)=0`

`RHL=lim_(x->0^+)=0`

`f(0)=0`

f(x) is differential only when LHD=RHD

`LHD=lim_(x->o^-)(f(x)-f(0))/(x-0)=lim_(x->0^-)((3x-0)/(x-0))=3`

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