Question: Prove that if is continuous and has no zeros on [a, b], then either f(x) > 0 for all x in [a, b] or

Prove that if ƒ is continuous and has no zeros on
[a, b], then either

f(x) > 0 for all x in [a, b] or f(x) <

f(x) > 0 for all x in [a, b] or f(x) < 0 for all x in [a, b].

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