Sorry, I was hoping the reference to Baby Rudin would be ok. I had forgotten that the theorem had a name. A jump discontinuity is a discontinuity where interme

Sorry, I was hoping the reference to Baby Rudin would be ok. I had forgotten that the theorem had a name. A jump discontinuity is a discontinuity where intermediate values are not attained, such as in the heaviside or signum functions. If a derivative exists at a point x, then it cannot have a jump discontinuity at x. However, it can have a discontinuity like the one exemplified by f(x) = 2x sin(1/x) - cos(1/x), with f(0) = 0, as that's the derivative of g(x) = x^2 sin (1/x)