IIT JEE , AIEEE Forum - Mathematics , Algebra

akhil_o

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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