# Answer to Question #19614 in Real Analysis for Matthew Lind

Question #19614

Continuity:

Let the function f(x) be continuous at every point of a closed interval [a,b]. Assume that f(x) > 2 for every x in [a,b]. Prove that there exists number c > 2 such that f(x) > c for every x in [a,b].

Let the function f(x) be continuous at every point of a closed interval [a,b]. Assume that f(x) > 2 for every x in [a,b]. Prove that there exists number c > 2 such that f(x) > c for every x in [a,b].

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