Seeking a tip on show to show convexity in a set.

Allow $f\colon \mathbb{R}^n \rightarrow \mathbb{R}$ be a convex function and also allow $c$ be some constant.

Show that the set $s=\\{x \in \mathbb{R}^n \mid f(x) \le c \\}$ is convex.

Hint : Well, simply list a convex mix of components in s and also validate that it come from s. You will certainly locate the convexity of f valuable for this.

Related questions