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## Homework Statement

Let f be a continuous function on the interval I=[a,b] such that for every x in [a,b] f(x)≠0.

Show that the function f(x) doesn't change its sign.( like increasing or decreasing)

## The Attempt at a Solution

Well for this to be true, we need to have f(a)>0 and f(b)>0 and f(x) is increasing so then it won't change the monotony. If we have f(a)<0 and f(b)<0, then f(x) is decreasing, hence we will not find any x in the interval I such that f(x)=0. Therefore for every x in the interval I f(x)≠0. Am I correct? Do I need to explain a bit more or what?

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