(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

True or false:

1) If f:R->R is a monotonically decreasing function then every discontinues point of f has finate right and left limits which are unequal.

2) I is some finate segment where a<b and a,b in R. If every continues function defined in I has a maximum and a minimum then I is a closed (in other words [a,b]) segment.

2. Relevant equations

3. The attempt at a solution

1) I think this is true but how can I prove it? Can someone give me a push in the right direction?

2)True: f(x)=x is continues and defined in any segment but it only has a min and max in an closed one. Is that right?

Thanks.

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# Homework Help: Monotonically decreasing function

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