Today I saw a theorem in class that stated the following:
$f$ is concave $ \Rightarrow\{z \in \mathbb R^n : f(z) \ge c\}$ is convex.
The proof is relatively straight forward and I understand. However, I have a hard time visualizing this idea to be true. I try and visualize the idea with a function such as $-x^2$ and I can't seem to see how the upper contour set is convex. If someone could walk me through a visual example with a graph that would be very helpful.