Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be defined as:
$$f\left ( x \right )=\left\{\begin{matrix} x^{2}sin\frac{1}{x}, & if x\neq 0, & and \\0, & if x=0.& \end{matrix}\right.$$
Which of the following statements is correct?
- $f$ is a surjective function.
- $f$ is bounded.
- The derivative of $f$ exists and is continuous on $ \mathbb{R}$ .
- $\left \{ x\in\mathbb{R} |f\left ( x \right )=0\right \}$ is a finite set.
