Let `f(x)=x^3+a x^2+b x+5\ s in^2x` be an increasing function on the set `R` . Then, `a` and `b` satisfy (a) `a^2-3b-15 >0` (b) `a^2-3b+15 >0` (c) `a^2-3b+15<0` (d) `a >0` and `b >0`

Explanation

`f(x)=x^(3)+ax^(2)+bx+5sin^(2)` x is increasing on R
`f(x)gt0forall x in R`
`3x^(2)+2ax+b+5sin 2xgt0forallx in R`
`3x^(2)+2ax+b+5sin 2xgt0forallx in R`
`3x^(2)+2ax+bgt5forallx in R`
`3x^(2)+2ax+(nb-5)gt0forallx in R`
`(2a)^(2)-4xx3xx(b-5)lt0`
`a^(2)-3b+15lt0`