Question

Let f : [a, b] → R and g : [a, b] → R be two continuous functions such that f(x) > g(x) for all x € (a,b]. 1. Show that there exists d > 0 such that f(x) > g(x) + 8 for all x € [a, b]. (Hint: introduce h := f -9] 2. Assume that g(x) > 0 for all x € [a, b]. Show that there exists k >1 such that f(x) > kg(x) for all x € [a, b].

Answer 1

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