Q. 65.0( 1 Vote )

Mark the correct A. a2 – 3b – 15 > 0

B. a2 – 3b + 15 > 0

C. a2 – 3b + 15 < 0

D. a > 0 and b > 0

Answer :

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

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