Interemediate Value Rule of Derivatives

If *y*=*f*(*x*) is continuous on [*a*,*b*], and *N* is a number between *f*(*a*) and *f*(*b*), then there is at least 1 *c* ∈ [*a*,*b*] such that *f*(*c*) = *N*.

That's actually the normal value. They're fundamentally the same.

So according to this, if I get it,

if y= |x| is differentiable at [-1, 1] then everything between the two is differentiable. But 0 isn't differentiable.

Something about my logic, if it's even worth calling that, is seriously weird.

Woulds someone explain my prob? Thank you!