Show that |c|<1|c|<1 ?
Given ff continuous , f:RR->RR
If f(x)!=0 for x in (-oo,c)uu(c,+oo) and
f(1)f(-1)<0
then show that |c|<1
Given
If
then show that
1 Answer
Jan 18, 2018
Solved.
f(1)f(-1)<0
According to Bolzano Theorem (generalization)
Supposed
- If
c>=1 thenf(x)!=0 ifx in (-oo,c)uu(c,+oo)
However,
CONTRADICTION!
- If
c<=-1 thenf(x)!=0 ifx in (-oo,c)uu(c,+oo)
However,
CONTRADICTION!
Therefore,