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!