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Hard continuity problem/proof  TOPIC_SOLVED

Let f and g be two continuous functions on the closed interval [0,1] such that for every x in [0,1] : f(x)<g(x). Prove that there exists some number m>0 such that for every x in [0,1] : f(x)+m<g(x). Well i think i have to use the fact that every continuous function on a closed interval is bounded by...
by smad
on Mon Oct 15, 2012 10:35 pm
 
Forum: Calculus
Topic: Hard continuity problem/proof
Replies: 3
Views: 2361

Re: Hard continuity problem/proof  TOPIC_SOLVED

Well if f and g are both continuous than therefore h=g-f is also continuous as a difference of 2 continuous functions and h>0 because f(x)<g(x). And the extreme value theorem states that if h is a continuous function on a closed interval [a,b] then there exists a c and a d such that h(c)>=h(x)>=h(d).
by smad
on Tue Oct 16, 2012 7:18 am
 
Forum: Calculus
Topic: Hard continuity problem/proof
Replies: 3
Views: 2361

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