Let $f(x)=x^3+ax^2+bx+5\sin^2x$ be an increasing function on the set R. Then a and b satisfy:

$a^2-3b-15>0$ $a^2-3b+15>0$ $a^2-3b+15<0$ a > 0 and b > 0

$a^2-3b+15<0$

$f(x)=x^3+ax^2+bx+5\sin^2x$ and $f'(x)=3x^2+2ax+b+5\sin 2x>0\,∀\,x∈R$ $⇒3x^2+2ax+b+5\sin 2x>0\,∀\,x∈R$ $⇒3x^2+2ax+b>-5\sin 2x⇒3x^2+2ax+b>5⇒3x^2+2ax+b-5>0$ $⇒4a^2-4.3(b-5)<0⇒a^2-3b+15<0$