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daniel_i_l
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Homework Statement
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.
Homework Equations
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.