Decide if the functions in parts 2-3 are differentiable at $x = 0$. Try zooming in with graphing technology, or calculating the derivative $f'(0)$ from the definition.
2. $f(x) = (x + |x|)^2 + 1$
3. $f(x) = \begin{cases} x^2 \sin(\frac{1}{x}) & \text{for } x \neq 0\\ 0 & \text{for } x = 0 \end{cases}$