Suppose that f is a continuous real valued function defined on the closed interval [0, 1]. Which of the following are true for constants C, D, E 0 and x, y ∈ [0,1] I. There is C such that |f(x) - f(y)|≤ C, ∀ x,y II. There is D such that |f(x) - f(y)|≤ 1, ∀ x,y that satisfy |x - y| ≤ D III. There is E such that |f(x) - f(y)|≤ E|x - y| ∀ x, y

Question

Suppose that f is a continuous real valued function defined on the closed interval [0, 1]. Which of the following are true for constants C, D, E> 0 and x, y ∈ [0,1] I. There is C such that |f(x) - f(y)|≤ C, ∀ x,y II. There is D such that |f(x) - f(y)|≤ 1, ∀ x,y that satisfy |x - y| ≤ D III. There is E such that |f(x) - f(y)|≤ E|x - y| ∀ x, y

Examsnet · Accepted Answer

Correct Answer is : Only IIIIIIIII

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