Consider the function $f(t)=(\max (0, t))^2$ for $-\infty<t<\infty$, where $\max (a, b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true?
- $f(t)$ is not differentiable.
- $f(t)$ is differentiable and its derivative is continuous.
- $f(t)$ is differentiable but its derivative is not continuous.
- $f(t)$ and its derivative are differentiable.