We consider the following curve in the interval $\psi:[-1,1] \to \mathbb{R}^3 $,
$$\psi(t) = \left(\frac{1}{3}(1 + t)^{3/2},\frac{1}{3}(1 - t)^{3/2}, \frac{1}{2}t\right)$$
I would prove that the slope of each element as it approaches zero ist the same in both directions and that it is continuous at $t = 0.$
Is there a specific method to prove the differentiability of a curve or is my assumption correct?