This is equivalent to a function f being derivable at a certain point, but the derivative is discontinuous.

Such a function or curve exists, but it is not a common function and needs to be specially constructed.

For example, f (x) = x 2 * sin (1/x), and f (0) = 0.

F is differentiable everywhere, but the derivative is discontinuous at 0. In other words, the curve (x, f(x)) is not smooth at the origin.