Mark the correct alternative in the following: Let f(x) = x 3 + ax 2 + bx + 5 sin 2 x be an increasing function on the set R. Then, a and b satisfy.

Question

Philoid · Accepted 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

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.

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.