- #1
Rosey24
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Homework Statement
We have a worksheet with practice final questions and I'm really stuck on this one on continuity:
Suppose h: (0,1) -> R has the property that for all x in (0,1), there exists a delta>0 such that for all y in (x, x+delta)[tex]\bigcap[/tex](0,1), h(x) <= h(y)
a) prove that if h is continuous on (0,1), then h is increasing.
b) Give a counterexample to show that this need not be true if h is not continuous.
Thanks so much for any help you can provide!