IF `f(x)=x^3+a x^2+b x+5sin^2x\ ` is a strictly increasing function on the set of real numbers then `a\ a n d\ b` must satisfy the relation `a^2-3b+15\ lt=0` (b) `a^2-3b+20\ lt=0` `a^2-3b+25\ lt=0` (d) `a^2-3b+30\ lt=0`

Explanation

`f(x)=x^{3}+a x^{2}+b x+5 sin ^{2} x `
`
d(frac{f(x)}{d x})=3 x^{2}+2 a x+b+5 sin ^{2} x=f^{prime}(x) `



For increasing function` f^{prime}(x)>0`
`

3 x^{2}+2 a x+b+5 sin 2 x>0`


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