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![[Post New]](/templates/default/images/icon_minipost_new.gif) 15 Apr 2008 10:16:35 IST
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SUPPOSE f(x)=x3 +ax2 +bx +c,where a,b,c are constants determined by throwing a dice three times.Find the probability that f(x) is an increasing function.
plz solve with explanation.
rates assured
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MONITH BISWOJYOTHI |
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15 Apr 2008 10:41:51 IST
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someone plz try this one
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MONITH BISWOJYOTHI |
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15 Apr 2008 12:29:03 IST
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f'(x)=3x2+2ax+b
for increasing function
f'(x)>=0
since a=3>0
this function will be positive for all values iff it has no real roots
b2<=4ac
4a2<=4*3*b
a2<=3b
see that c does not affect nature of function
so for all a2<=3b, it holds
b a
1 1
2 1,2
3 1,2,3
4 1,2,3
5 1,2,3
6 1,2,3,4
so we have 16 cases where this holds
P=16/6*6
=4/9
also note: for monotonically increasing function(where f'(x)=0 does not work)
a=3,b=3 soed not work
P=15/36=5/12
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16 Apr 2008 08:24:26 IST
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hey akhil didn't understand da way u solved
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MONITH BISWOJYOTHI |
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