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Let $f(x) = ax^2 - b |x|$, where $a$ and $b$ are constants. Then at $x=0, f(x)$ is,

1. maximized whenever $a>0, b>0$
2. maximized whenever $a>0, b<0$
3. minimized whenever $a>0, b>0$
4. minimized whenever $a>0, b<0$

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