Question 844359
{{{ graph( 300, 300, -5, 5, -10, 10, abs(x^2-4)) }}} 
From the left {{{x<-2}}}, function looks like, {{{f(x)=x^2-4}}}
{{{df/dx=2x}}}
{{{lim(x->-2, (f(x)))=(-2)^2-4=0}}}
{{{lim(x->-2,(df/dx))=2(-2)=-4}}}
From the right {{{-2<x<2}}} the function looks like {{{f(x)=-(x^2-4)=4-x^2}}}
{{{df/dx=-2x}}}
{{{lim(x->-2, (f(x)))=4-(-2)^2=0}}}
{{{lim(x->-2,(df/dx))=-2(-2)=4}}}
So although the function is continuous, the value of the derivative approaches -2 from the left and right are not equal so it is not differentiable.