Looking for a hint on show to show convexity in a set..
Let $f\colon \mathbb{R}^n \rightarrow \mathbb{R}$ be a convex function and let $c$ be some constant.
Show that the set $s=\\{x \in \mathbb{R}^n \mid f(x) \le c \\}$ is convex.
Looking for a hint on show to show convexity in a set..
Let $f\colon \mathbb{R}^n \rightarrow \mathbb{R}$ be a convex function and let $c$ be some constant.
Show that the set $s=\\{x \in \mathbb{R}^n \mid f(x) \le c \\}$ is convex.
Hint: Well, just write down a convex combination of elements in s and verify that it belong to s. You will find the convexity of f useful for this.