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If graph of the function f(x) =3x^(4)+2x...

If graph of the function f(x) =`3x^(4)+2x^(3)+ax^(2)-x+2` is concave upward for all real x, then find values of a,

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We have f(x)=`12(x)^(3)+6x^(2)+2ax-1`
and `f(x)=36x^(2)+12x+2a`
Now graph of concave upward for all real x.
`therefore f(x)=36^(2)+12x+2agt0 forall` real x
Discriminant , `12^(2)-4(36)(2a)lt0`
`rArr 1-2alt0`
`rArr agt1//2`
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