Question
(3) Suppose that f : R2 → R is a continuous function at x0 ∈ R2 and that |f(x0)| > 2. Show that
there is a $ > 0 such that |f(x)| > 2 whenever ||x − x0|| < $.
there is a $ > 0 such that |f(x)| > 2 whenever ||x − x0|| < $.
Answers
Steve
Isn't this just the intermediate value theorem in disguise? f is continuous.