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Let f(x)=x^3+a x^2+b x+5sin^2x be an inc...

Let `f(x)=x^3+a x^2+b x+5sin^2x` be an increasing function on the set `Rdot` Then find the condition on `a` and `b`.

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`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`
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