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Mark the correct alternative in the following:
Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.
Formula:- (i) ax2+bx+c>0 for all x a>0 and b2-4ac<0
(ii) ax2+bx+c<0 for all x a<0 and b2-4ac<0
(iii)The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)
Given:-
f(x) = x3 + ax2 + bx + 5 sin2x
For increasing function f’(x)>0
3x2+2ax+b+5sin2x>0
Then
3x2+2ax+b-5<0
And b2-4ac<0
4a2-12(b-5)<0
a2-3b+15<0
a2 – 3b + 15 < 0