The function f:R rarr R, f(x)=ax^(2)-b|x...

The function `f:R rarr R, f(x)=ax^(2)-b|x|, a, b in R` has a local minimum at `x=0` then which of the following options must be CORRECT?
O `a>0`
O `b<0`
O `|ab|+a|b|+b|a|=-ab`
O `|ab|+a|b|=b|a|+ab`

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