\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the piecewise function \(f\) defined on \(\mathbb{R}\) by:$$ f(x) = \begin{cases} x^2 & \text{if } x \le 0 \\ x & \text{if } x > 0 \end{cases} $$
  1. Show that \(f\) is continuous at \(x=0\).
  2. By comparing the slopes (derivatives) on the left and right of \(x=0\), explain why \(f\) is not differentiable at \(x=0\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.